 Let us take next set of questions okay you can start attempting these I will put one more did we do this and this one the earlier one no do that oh that is the reason why we did hmm both of them complete so this is option to write right next one I think this is straight forward just you know you should know it 18th why the electrical conductivity of semiconductor increase because of the radiation no let's talk about the valence and conduction band related to that because they can jump right because only conduction electrons are responsible for conductivity right so you need energy corresponding to this wavelength for them to jump this is like minimum energy required for them to jump okay this is like valence band and this is conduction band okay so energy corresponding to this can be absorbed by the valence cell valence band electron and this electron may jump to conduction band okay how much energy is required is actually equal to the band gap right band gap by definition is the minimum energy difference between conduction and valence band this is EG how much is this quickly option 3 0.5 okay so see this is how you solve it at C by E lambda right this is energy in terms of electron volt okay H is 6.6 into 10 minus 30 why I am showing you how to calculate because this will come again and again this type of calculation this divided by 1.6 into 10 is power minus 19 wavelength is what 2.48 into 10 is power minus 6 right now you can see that this is almost 4 times so 6.6 divided by 1.6 is like frequent frequently it will be coming so this is near 4 slightly more than 4 so just remember that it is slightly more than 4 okay and 6 plus 19 is 25 plus 8 33 33 so you just cancel all of this I just put 10 is power minus 1 okay now see it become 12 divided by 2.48 which is like what 12 divided by 2.5 right 12 divided by 2.5 2.5 is what around 5 by 2 okay this into 10 so minus 1 now this is 5 to the 10 2.4 so around it is coming 0.48 right so like this you can roughly estimate the value so don't get overwhelmed by so much calculation you can easily handle right that is our option number 3 is correct why divided by E electron volts fine next question this we have done this one solve this one all of you any other any other any answer option B where is B okay now first tell me which one of them is more stable this one or that one this one is more stable why give me some logic why do you think I am asking you which one of these two nucleus is more stable okay do you have any logic that okay this is more stable because of this whatever you have learned don't create a logic okay whatever you have learned based on that tell me which one of them is more stable copper 30 why what see they there lies the problem see here you are looking at the electronic configuration okay but we are talking about nucleus here chemically it will be more stable but I am talking about stability of nucleus not the electrons okay so which nucleus is more stable because all the decays they happen for the nucleus not for the electrons second one is more stable why exactly so see what happens in both the cases 64 protons or neutrons protons or neutrons okay 64 of them they combine to produce either 29 copper 64 or they produce 30 copper 64 okay now mass of this is lesser mass of these 64 proton and neutron it is same both the cases okay so the mass difference between this and that is more so more mass is converted to energy are you getting it so that is the reason why this is more stable because it is actual mass is lesser so more mass would have got converted to energy and that is why it is more stable okay so you can say that it is like both are exothermic reaction and more heat is released in the second reaction like that you can understand okay so now if there is a decay who will decay the lesser stable one who is lesser stable copper 29 right so okay one more thing one of them is copper another one is zinc because both of them can't have 29 atomic number so let me just check which one of them yeah but the element is different who is atom zinc atomic number do you know zinc is 30 copper 29 so this is zinc this is not copper this is zinc okay so copper will decay zinc will not decay right so this is out of question and if it is a gamma decay then atomic number will not get affected right here atomic number is getting affected so even this is not true so this is most suitable answer getting it because zinc is more stable right it's a natural tendency that you go from lesser stable to more stable one okay what you are talking about if it was cu 64 cu 30 doesn't exist 30 atomic number is zinc printing error what stability why is he said that cu 20 sorry zinc 30 is more stable cu 30 there is nothing called cu 30 it was a printing error okay so zinc 30 is more stable so copper will decay into more stable form zinc start solving the question do you remember question number last one solve these two questions 20th is fourth see for hydrogen energy in nth orbit is minus 13.6 by n square for hydrogen like atom energy in nth orbit is 13.6 by n square into z what is z atomic number okay so energy required to remove electron from ground state of doubly ionized helium is what how will go about it I'm asking what what is NF NF is infinity right so energy when energy of electron when it leaves the nucleus when it when it has just sufficient amount of energy its potential energy will anyway become zero it goes to infinity right and minimum energy required will be such that even its kinetic energy becomes zero okay so energy of the lithium lithium atoms first electron will be what 13.6 sorry lithium atoms electron which is in ground state is one square into nine three square is nine this much electron volt is its energy which is negative and if I want to make its energy zero what should I do have to do this much energy have to supply so that total energy becomes zero no that is not ionized ionized means the electron leaves and goes away that means it goes to infinity 21 yeah of course why not Kirchhoff's loop rule is valid anywhere we have solved alternating current questions also Kirchhoff's loop rule and general rule they are just conservation of charge and one point cannot have so potential where is b 2 second option isn't this something which is straight how much current is flowing this loop zero so this is you just throw it away this one including resistance you throw it away the current is flowing simply like this all the currents okay it will be as if 150 plus 100 are in series okay so the current will be what tell me this is 6 what yes tell me how will you get current is equal to what tell me how will you write 6 divided by 100 plus 150 plus 50 okay now here there is a small assumption the assumption is the the you know the forward bias doesn't offer any backward voltage but there is a small 0.7 volt all right so actually you should write 6 minus 0.7 divided by all this but we are ignoring that fine so just be aware of that this is 6 divided by 300 how much is this 1 0 2 all of you understood this should I move to next one these two black background is better right option 2 3 yes this also is 23rd first one I mean see first of all respect the question h mu minus at least you should write this formula this at least okay so stopping potential is asked so this is k max right which can be written as e into v v stopping potential so stopping potential is what h mu minus phi divided by e so maximum current energy of photo electron emitted from a surface is 4 electron also oh so basically e into v itself is given 4 electron volts so v will come out to be 4 volts right so option number 2 is correct but at least write something don't just run over it unless you have seen similar question already okay because chances are high that there will be a small trick hidden which you skip the steps you lose the trick and will not earn zero right you know that you'll get minus one start doing this question I'll upload the other one 23 so you can see many theoretical questions are asked 24th what is the answer correct so it's a probabilistic event we cannot be definitive about it it may or may not decay 25th okay for this you can actually draw a p in junction first talk about 25 this is the junction is p this is n okay now see here you need to evaluate the options here you need to evaluate the options okay so you cannot just ignore all the options so you can't just solve this and get the correct answer right you have to check which of the options make sense so you need to read actually all of it so probably all the options are talking about just electric field so you need to just look at the electric field but some options talk about electric field some talk about potential okay now if I know that only single option is correct I'll first look at the easiest of all which is what finding the electric field okay right now because I have drawn that so we have electric field like this any doubt here right so electric field should be from n to p right so option 3 is correct so if it is a single option correct I'll just move ahead okay otherwise if I have to look at the potential also then which will have higher potential n has higher potential right positively charged slightly higher potential okay but there is no current why there's no close circuit okay it's like a battery keeping battery five volt battery but then voltage is there current is not there fine let's move to the next one have you seen that x-ray video which I have given solve this there's 20 every time there is power failure frequently they ask questions on x-rays so it is for your benefit to watch that video which I have solved 20 26 first tell me that how many of you seen that video okay 26th is 2 okay so we have for x-ray graph like this right those who have seen it can relate it starts from this minimum wavelength and it goes on this is like intensity of the radiation for different wavelengths which comes out these two are characteristic x-rays k alpha k beta characteristic wavelength now once you watch that video you will understand it okay anyways 27th anybody dead three three three the work function of a substance is four the longest wavelength of light that can cause photoelectric emission that's I think straightforward all you have to do is you know that work function is this much so at least you need this much energy so at least this much frequency so minimum frequency is largest wavelength okay so just equate hc by e lambda with four okay from here you'll get lambda to be equal to hc by four key okay which will come out to be see you know when you divide charge of electron with h factor of four comes then divide by four also so I think it should be around speed of light into some 10 which are something so three should be there so that's how you can so h by e will give you first digit as four and four by four around one yeah for exactly one and then speed of light this it has three in it okay but don't use these kind of things if you are not very if you have not done a lot of practice don't force yourself to do like this be honest with yourself otherwise you'll make a lot of serious 20 okay now let's see let's first look at these let's first look at these four nuclei okay which one of them is most stable why is most stable right so if lesser stable one becomes more stable it will be a spontaneous process and it will release the energy also I mean it will not be spontaneous maybe there is activation energy but then yeah it will release energy ultimately because lesser stable to more stable right now look at the first one why is giving 2z why is more stable 2z it'll absorb energy okay look at the second w is giving x plus z now x is more stable but z is less stable so you can't be sure about it okay look at the third one w giving 2y now this is sure shot when w gives 2y definitely it is going to be more stable okay and you'll have option number three to be correct would really is a definitive statement it is not saying merrily is energy okay so let me do one thing you don't have to scroll too much lots and lots of theoretical questions that have asked in jay 29 and 30 9 valid 29 29 29 what is the answer online class with the photo there was this guy I was taking online class so in your which book I refer to so yeah I got him I got him I it was question number seven or eight in my list and in that book it was question number five so he said five option for his career wait let me talk to you so it's it's a very very bad and very so to say it's a you're damaging your prospect and also you are making everybody else feel that okay they don't know many things like how come somebody is suddenly become so intelligent but actually what happens is that that guy was making fool of himself okay so there will be a lot of such cases so just do your best okay that's all you can do right anyways so why do be a lot of there should not be any worry as such okay 29th which one see you should be knowing it as a matter of fact how if you have read your ncrt book and if you know that r is equal to r not a to the power one by three and the value of r not if you remember the density is independent of the atomic mass or atomic number it comes up to the order of 10 square 17 so they expect you to remember this okay anyways for any element it's independent of the atomic if it is independent then for any elements it is independent the nucleus is so tightly packed reading it i mean if there are more number of nucleons more volume will be there but density is independent 30th what is neon's atomic number 10 it after absorbing energy decays into two alpha particles so two alpha particle so it gives this so what will be this suppose this is x so what will be the atomic number six so atomic number defines what the element is mass number doesn't define it's car oh this is Doppler effect question number 30 31 yeah i'll just directly tell you the formula and anybody knows this okay write down the formula is delta lambda there's a derivation also to it will not get into that this is equal to v divided by speed of light okay what is what is it's hydrogen spectrum right it's alpha is it's it's one of the wavelength one of the characteristic wavelength of hydrogen spectrum okay now the same wavelength same as in the same em wave has a different free different wavelength observed and actual so you can use this formula directly over here lambda naught is the original wavelength v is the speed with which galaxy is moving away b so v is speed of light multiplied by difference in the observed wavelength and the actual wavelength is how much 706 minus 656 okay divided by the actual wavelength 656 okay so when you calculate this you'll get c into what numerator is 50 50 divided by roughly the new denominator is also 650 roughly okay and then this is 13 okay so basically you're doing 3 into 10 is power 8 or let's say 3 divided by 1.3 into 10 is power 7 so 3 divided by 1.3 so you don't have any problem in the first digit right all the options have 2 in it so the it's just the 10 is a power of what it is it has to be second fine we'll move to the next one this one 30 second second no three three sign me with a doubting the question how dare you huh once you get a question you solve it or you just all of you try what is the first step here like what what is the bottom line which you should use conservation of momentum energy may not mechanical energy may not be conserved some part of it will get lost as heat so the momentum of the two particles will be equal and opposite yes or no because initial momentum was 0 right so moment magnitude of momentum of m1 is equal to magnitude of momentum of m2 let's say that is p isn't it because some of the momentum vector sum should be 0 so magnitude wise they should be same okay so if one goes this way other will go in opposite way with equal momentum any doubt here no now deeply wavelength is what h by p now momentum is same so wavelength will be same no momentum doesn't depend on mass sorry wavelength doesn't depend on mass wavelength depends on momentum multiplication of mass and velocity see this is total mass m1 and m2 okay initial momentum of m2 is 0 so when it breaks into m1 and m2 it's like explosion sort of okay so initial momentum of m1 m2 or 0 it should be 0 afterwards also whatever the force it is internal between them there is no external force that is a momentum of m1 will be equal to momentum of m2 fine so let's move to the next one let's look at the theoretical questions in this chapter so at times you think that physics is only numerical but that's not true this is 33 34 33rd which one one option one yeah two air you're telling me two no time here how did there is two gamma rays are em waves okay they are not particles this is definitely not correct they are like highly energetic em waves okay then is also particles singly ionized doubly ionized proton and neutrons as no although beta has beta minus and beta plus beta minus is cathode but in general you can say okay fine one of the beta rays is cathode 34th can I what increase the size ask her she knows now it is fine three half-life period of radioactive element is same as a mean life of other initially both of them have same number of atoms three all of you every step it's okay should I solve it it's a t half of x is same as the mean life of y okay so 0.693 divided by lambda x is equal to one by lambda y so lambda x is 0.693 times lambda y fine initially both of them have same number of it atoms same number of items means same number of nucleus also okay so you twist here what if I tell you that there are two compounds x and x2 both of I mean suppose this is x the first one and second one is y and I say both of them have same number of molecules then one molecule of this has two nucleus getting it so which you write dn by dt is equal to lambda n n is number of nucleus not number of compounds you have to count how many nucleus are there fine so remember all that let's do this first now initially both of them have same number of items then whose decay rate will be I mean decay rates will be different because lambda is different now decay rate is what dn by dt is equal to minus lambda times n okay so if it is n so for x it is lambda x into n for y it is lambda y into n which will be more lambda x will be more see lambda y sorry lambda y will be more lambda y is more right so y's decay will be faster than x that is my option 3 okay so lambda y is lambda is divided by 0.693 which is more than lambda x lambda x is less than lambda y fine okay simultaneously we have covered that in theory that x gives y and then y gives z so I am about to do that this is what question number that is now you will not be able to do this because you haven't gone through that when you will be sincere with your preparation when you'll start doing that any plans see I'll just I think I've briefed little bit last class this time again I'll tell you that the characteristic x-ray will be created only when electrons from the target element get knocked off now do this and how continuous x-ray gets emitted the electrons is coming from outside will get decelerated because of the interaction with the target elements electron and its nucleus so because of the deceleration its energy goes down so difference energy photon gets emitted that is continuous x-ray now when it is characteristic x-ray these electrons come from outside like for example 80 kilo volt kilo electron volt that will knock off one electron from the tungsten and then transition from higher shells to from where it has knocked off will happen and that will release a photon that is characteristic x-ray so characteristic x-ray has nothing to do with what was the energy of the electron coming because the energy gap is between the shells of the tungsten but that continuous x-ray is because of the energy of the electron that are coming from outside it is getting slowing down slowed down and because of that you know you have to I mean to be comfortable with this you have to watch that video once what is the answer here you're saying option one any other answer as a will it have a characteristic x-ray or not yeah can it knock off an electron or not 80 kilo electron volt it can knock off there will be a characteristic x-ray option four there will be a characteristic x-ray okay and then how will you find minimum wavelength when all the energy of the electron electron completely loses its energy and that energy which which was coming towards the atom that gets converted to photon okay so now do that let's see whether you get 0.155 minimum wavelength so that is why there is a minimum wavelength of continuous because electron when it comes it will have some energy okay so maximum possible frequency will be emitted when all the energy of the electron gets converted into photon simply have to do at c by approximately that so you know whenever this h comes and there is one point say you can just cancel out and say it is four over so you can calculate lambda so when all the energy of the electron gets converted into photon that's when you have lambda minimum or maximum frequency okay option four is correct okay how do you find questions on modern physics compared to other chapters but then if you if you if you like you know take it for granted if you start taking like fine these are like simple chapter let me do it towards the end i'll be able to do it you'll not get these it's not that easy also that will be just ignore it and you'll towards the end will just master it it can't but then that's why i'm telling you your your good amount of time should get into or should go into the chapters which are easy and which you think you can master easily okay start doing stop doing chapters which you have very little idea of don't try to learn anything new whatever you know strengthen it getting it 60 marks in j mains is very good don't run behind those extra 10 marks and then your entire 60 70 marks which you will get that will suffer okay there is 30 actually here you should have a knowledge no you cannot just i mean otherwise you need to derive from the scratch mv square by r is equal to okay so you should have some knowledge of how you write the wavelength so 1 by lambda is what rickbook constant 1 by n1 okay now your rickbook constant is proportional to your rickbook constant is proportional to mass your rickbook constant changes depending on which element it is because if it is for height doesn't it is 1 sorry rickbook constant into 1 now here it is two times so rickbook instead of rickbook constant you write 2 r h are you getting it so like that you have to write or you use the fact that energy is proportional to mass energy in nth level which is right 13.6 by n square okay so this is rickbook constant into 2 now here you have what a transition from way to where first accept first accepted levels first accepted level is what and is equal to 2 and longest possible means from 2 to 3 so 1 by 2 square minus 1 by 3 square lambda is shortest for when second goes infinity lambda shortest means 1 by lambda is longest lambda longest means 1 by lambda is smallest so 1 by lambda is 2 times rickbook constant 1 by 4 minus 1 by 9 so lambda will come out to be 18 by 5 18 by 5 5 are in denominator right number three okay so in modern physics those derivations you know in your school book or whatever it is you are very comfortable with hydrogen atoms so if someone wants to make a problem which many could not solve you can't make a very tricky question so what they do they make questions based out of whether you know something or not okay so look at the derivation very closely how it is derived then only you'll be able to say that okay fine energy should be proportional to mass also or how atomic number comes in that you should know how atomic number comes or what I mean right so what all those m when you write mv square by r is equal to g m1 m2 by r square and when you write potential energy counting energy so get into details of it because knowledge is more important in these chapters than your analytical scales fine so let's move to the next one and it out this 37 right anybody else should you have the bum today oh happy birthday so she is having party at home she didn't call you okay modern physics so like full day party okay now I'll start solving so decay constant for x1 is 10 lambda decay constant for x2 is lambda they need to find ratio of number of nuclei of x1 to that of x2 so number of nuclei for x1 is n0 e to the power minus lambda 1t and nx2 number of nucleus are same initially so this now the ratio of number of nuclei is equal to e to the power lambda 2 minus lambda 1 into t okay now it is asking you x1 divided by x2 okay so lambda 2 is lambda lambda 1 is 10 lambda okay so this is e to the power minus 9 lambda t any doubts e to the power minus 9 lambda t you need to find when this will become e to the power minus 1 so t will be equal to 1 by 9 lambda that's why option 4 okay in doubts fine we'll move to the next one 30 option 2 any other answer total energy remains same this kind of difference don't tell I taught you this chapter see total energy total energy is what total energy in nth orbit is 13.6 by n square electron volts right so total energy will what when it goes to ground state from excited state what will happen to total energy it's it will decrease it becomes more negative so it will decrease now what see kinetic energy is what now look at how kinetic energy is defined kinetic energy is what in terms of total energy is positive of total energy and potential energy is what two times of total energy getting it so this will become minus of 27 by 2 by n square electron volt this is potential energy kinetic energy is plus 13.6 by n square electron volts so when you add it you get total energy getting it kinetic energy will be positive it can't be negative now when you're decreasing n from 2 to 1 it goes right so it's kinetic energy what happens to it increases kinetic energy increases excited state to the ground state when n becomes 1 kinetic energy is 13.6 electron volt and earlier it was 13.6 divided by 4 electron volts so kinetic energy increased so this is out of so like that you know you can just now it is between one and four so kinetic energy will kinetic energy increases potential and total energy decreases okay so like you know there will be multiple checkpoints when you solve a question once you arrive one landmark this thing immediately look at the option and remove start rejecting the options so that you can narrow down to the correct one faster okay and you know the the revolution of electron and nucleus is very similar to the planetary movements around the sun so you can imagine like you know mars being very close to sun it revolves very fast okay as you move closer to the sun gravitation force becomes very strong or the centripetal force becomes very small okay so a velocity should be very high to create that acceleration towards the center i mean okay we will move to the next one okay upload another one 38 right 39 no this is more important 39 39 39 which option the electron that comes out in a beta decay it is not your outer shell electron okay the neutron becomes proton and because of charge conservation electron electron will first generate inside the nucleus and then it will come out because nucleus is unstable with electron in it okay now 40th hey for apple you remember i have circulated one message on the group yes what was that but yeah yeah bummer is limon limon is uv and passion Lime man means what? Lime man is transition from or to? to what? to one, to one, right? This is for this is for hydrogen light atom, this is not for hydrogen atom. So, this is this is for hydrogen atom, okay? For hydrogen light atom transition from n equal to 4 to 3 results in uv, okay? So, let's say 1 by lambda is a Rigberg constant into z square from 1 by 3 square minus 1 by 4 square, okay? This results in uv and uv should be Lime man, right? So, here it should be 1 by 1 square should come. So, z becomes 3, okay? So, like that you can you know roughly figure out. Now, z becomes 3. So, now what you should get infrared? So, why z3 again? This is uv series 1 by 1 square minus 1 by n square, right? So, if you correlate z should be 3, okay? Now, I should get what? Inferred is what? 1 by Rh 1 by infrared is Lime man bomber passion 3, right? 1 by 3 square minus 1 by whatever n square, okay? So, here the first one should be 1 by 3 square it should come, right? We know that 3 square is anyway outside, okay? So, if 3 square has to come outside then it be 3 into 3, right? See, 2 to 1 is anyway out of question because it will be higher frequency. 3 to 2 is also higher frequency, okay? Even 4 to 2 is even higher frequency, right? The only option left is 4. So, like that you can just arrive at the final answer by rejecting it again x-ray. But I think we have discussed enough for you to answer this question. 40, 41. This is lambda k, characteristic wavelength. No, wait. Intensity of x-ray, Coolidge tube, minimum obtained is lambda c, variant of k alpha is lambda k. So, this, you know, k alpha is this characteristic wavelength. One of the characteristic wavelength is k alpha, the first one in fact is k alpha. Check, check what it is. So, now tell me what is the answer? The option is that lambda k minus lambda k. Yeah, minus, minus. Okay, that's it. Should we discuss now? So, when you increase the accelerating voltage, what happens to the electron that is coming from outside? It will have more kinetic energy. So, you have more available energy to create a photon. So, minimum possible wavelength or the maximum possible frequency will come when entire kinetic energy gets converted into photon. So, if energy increases, lambda c will decrease. Lambda k anyway doesn't depend on accelerating electron. Lambda k will be fixed. Lambda c will decrease. So, lambda k minus lambda c will increase. Option one, okay. You want to eat, you can have it. It is what? No, but you will not be able to. Her entire mind is there, okay. My food has come. Anybody else's food coming? So, her parent loves the most. Okay, so, she cooks like the fresh food, like everybody else will bring in the morning, but your mom will like every hour one packet should go. Then, is that what you call it? Sentum lunch. Wow, why sentum lunch? Your mom will hate when there is a sentum this thing. She has to cook more, right? So, you will be like negotiating with mom. Today in sentum lunch, I want something like that, right? That's what you are checking that whether it is there or not. She is very kind to take the food and give it to you. You know why? Okay, what is the answer? Don't talk nonsense. Okay, it has two distinct species. Having equal number of items initially, mean life of one species is tau, other one is five tau. The decay product in both cases are stable. It doesn't disintegrate further. The plot is made of the total number of radioactive nucleus as a function of time. Okay. Now, as the time increases, we need to find the number of radioactive nuclei as in how many are left? Will it decrease with time? Will it remain constant? Will it ever increase? No. Option four, right? Here, see, suddenly it starts increasing. Here it did and there it remains constant. Okay. So, if you really want to think too much, they'll give you reasons to think, but you'll be thinking in the wrong direction. So, if you keep things simple, you'll get the answer. What did it do? Okay. What is third? What is the number of electrons striking the target? Whatever electrons are striking the target, the current is because of them only? Okay. So, 3.2 milliampere, which is this much ampere, it should be a charge of electron, which is 1.6 into 10 to the minus 19 into number of electrons striking per second. Fine. So, from here, you get the answer and you can look at it. The difference is in 10 to the power. So, you can just find out what is 10 to the power, this thing. It should be 10 to the power 16, right? So, in any way straightforward, there is 2 and then 2 into 10 to the power 16. Okay. 44th. Second one. Second one. Angular momentum does not depend on the atomic number, right? NH. Right? It is NH by 2 pi. So, angular momentum should be same, but energy depends. Right? But here, mod of energy is compared. Still. Still. So, 13.6 by N square into Z square. This is mod of energy. This will be more than 13.6 by N square, if you just talk about absolute value. But if you just talk about total energy, then actually it is less because it is more negative. But since you have taken mod, energy of the lithium will be more. I just mod of that. That's our option 2. See how they trick you. Like, if you are in a hurry, okay fine, let me tick 3 and move on. Minus 1. So, plus 4, you get minus 1. So, 5 marks difference. Okay. We'll move to the next one. Start doing it if you are able to read. 44. What is 6? What if I raise? 116th means what? 16th. The activity is going down by 116th and activity depends on how many radioactive nuclears are there. Right? So, if activity is N, sorry, activity is proportional to the number of nuclear, right? So, if activity has to become half, N naught should become N naught by 2. Then, if activity has to go to N naught by, sorry, again half, it will be like this. So, like that, you can see that. Now, how many times it becomes half? 1, 2, 3, 4 times. Right? So, 4 half-lives it will take. Okay? So, 100 into 4. 400. 46th. 3. 3. Gamma is E m by m. Neither atomic number nor mass number. Now, tell me one thing. This nucleus, okay? This one is one nucleus. They are the same. They are the same nucleus. Are their masses same? Why? So, energy. Right. So, you should write it like this x star. This is at higher energy. Even though it is exactly same number of protons, neutrons and electrons, but then mass of that is slightly more than the ground state mass. So, that is why you will see a term like rest energy or something like that, okay? Because if it has a kinetic energy or it has an energy, its mass will be different, okay? So, be mindful of the fact that the difference, the mass defect is equal to energy of the gamma ray here. Fine? So, h mu is equal to delta m c square. It will be very, very small, but even the small will create a lot of energy, small defect. Electron? Yeah, yeah. Joule is of course much bigger than electron volts, but then you have to also understand that electron volts we use for typically electrons energy or nucleus energy. Now, I am saying one electrons energy is two electron volts, okay? And how many electrons will be there? Suppose for example, this bottle. There are like so, so many, right? It is more than 10 to the power 30, 40. So, just multiply with that like it becomes huge, okay? Now, typically in nuclear reaction we are talking about mega electron volt, 10 to the power 6 times more energy. So, because of multiplication factor is huge even though electron volt is a very less energy, but electron itself is a very, very small and there will be so many electrons will be there. Fine? So, ultimately when you multiply, it becomes tremendous amount of energy. 47. You know this formula r naught n square by z square. I remember it z. Yeah, it is z. Same chapter is there in chemistry also, structure of atom. 100. All of you. Both radius is what? Radius of, radius of hydrogen atoms electron which is at n equal to 1, which is r naught only. Last orbit is what? For, for this element, what is the last orbit? n. What is n equals to? That is what you get n square and the LHS at the end in the RHS. No. This n is principal quantum number. It says that atom follows a Bose model and the radius of the last orbit of this is n times. Let us make it x, okay? It is x times. Then what is the value of x? You are confusing between n here and principal quantum numbers. Now tell me, what is the value of last orbit's principal quantum number for this element? VFR? Tell me, what is the principal quantum number of last orbit? Do you know you can write it like this 1s2, 2s2, 2p6? Like that you keep on writing this number represent principal quantum number. So, what is that for atomic number 100? What it should be? 6p6. What is this called? When you write 1s2, 2s2 like that? Electronic. Which electronic configuration is there in this? 6p6. 6p6. This is 7. Max will go to 7. So, you can write like this down 5f12 7s2. I mean it is a knowledge based thing actually. Nobody will be going up to this level of thing. Anyways, so 7 is the outermost principal quantum number, right? So, this becomes 7 square divided by what is atomic number? 100. So, this is 49 by 100. So, roughly it is, are you sure it is z not z square? I think you have to assume it. I will come back to this. There is some confusion in the wordings of the question. Let us leave it. What about 48th? Why? Density should be constant. If density is constant then mass by volume should be constant. So, mass should be proportional to volume. This is 49 heat. I do not know what you are saying. No, binding energy formula. 1 AMU corresponds to 931 MeV. 54, right? 24,000. I understood. 49 crore. Do both of them then tell me the answer. 50th, all of you are getting 4th? 50th is the easier one. I mean calculation wise. You should do that first. Disintegration per second is DPS, but the rate is proportional to number of nucleus. Should I do it? 50th? So, let us say x DPS is at 3 equal to 0. After 280 days, it goes down to 6000 DPS and then after 140 days it drops to 3000. So, what we can infer from here? Half-life is 140. So, it was anyway 2 half-life away, 6000. So, 6000 should be x divided by 2 raised to power 2. See, 6000 is 2 half-life away from x. It becomes half 2 times. So, that is a x by 2 would be 140, again by 2 in next 140. This is 6000. So, the value of initial disintegration rate is 24,000. 49th, what is the answer? Guessing it? How you are doing it? He was binding in delta is equal to delta m into c square. Where is delta m? There is no delta m. It is a alpha particle. So, mass has to reduce by 4. Okay. So, delta m will be 4 atomic mass. No, no, no. It is not that alpha got directly converted to energy. Should I do it? So, I will first give you a hint. Suppose this is A. This is a nucleus. A is generally the mass number, right? So, I will take it x. So, we have x whose mass number is 220. It decays into alpha particle, which is helium 4 2 plus another particle will be there. Let us say y, right? Here, what should be the mass number? 216. This is a reaction and heat released q. This is the heat. Now, tell me what is this heat? Heat is the tiny technology of the atoms only? Right? So, 5.5 MeV is kinetic energy of helium plus kinetic energy of y. Any doubt here? Okay. What else can I do here? What else? Wait. This was at rest, no? Momentum will be conserved. Momentum of helium should be equal to momentum of y. Okay. Okay. So, kinetic energy of helium, let us say momentum is P. So, I can use P for both because they are same. So, I will take a pause here. Solve it yourself. So, kinetic energy of helium is P squared divided by 2 times mass of helium, right? And kinetic energy of y is P squared by 2 times mass of y, waiting here. So, kinetic energy of helium divided by kinetic energy of y. How much it will come? Mass of y divided by mass of H e. Mass of y is 216. Mass of helium is 4, right? So, this is 54, right? So, k helium is 54 times k y. Okay. So, just substitute there. You will get 55 times k y is equal to 5.5. Okay. So, kinetic energy of y is 0.1 MeV. All right? So, if kinetic energy of y is 0.1 MeV, kinetic energy of helium is 54 into 0.1, which is 5.4 MeV, option 2. Okay. Right? Any doubts?