 So again, completely different type of questions from your routine problem practices. So, that's how the questions will be asked from the modern physics. Now, let me see some latest questions. This came in J-Advance 2013. It's an integer type question. A freshly prepared sample of a radioisotope has a half-life of 1,386 seconds. And it has an activity. Activity is what? Dn by dt, isn't it? So, dn by dt is given as 10 raise to power 3 is integrations per second. So, these are the two values given. Now, natural log 2 value is also given, which is 0.693. I think you know it already. Anyways, you need to find out fraction of initial number of nuclei. You need to find fraction of initial number of nuclei. As in what fraction of initial number of nuclei will decay in first 80 seconds after preparation of the sample? In 80 seconds, what is a fraction of initial number of nuclei that will decay? Are you able to understand the question or you want me to repeat? No, sir. Once you get the fraction that into 100, you have to do and put your answer as a percentage. Fraction will be less than 1, of course. Sir, 1.88%. No. So, 53.9%. How can it be? Half life is 1,386 seconds. And you are saying in 80 seconds more than half will be decayed? Sir, yeah, but like I am getting that. No, that's not. See, we have this formula, right? ln n by n naught is equal to minus lambda times t. What is n? n is a number of nucleus that are remaining. So, ln n by n naught comes out to be minus of 0.693 divided by t half, which is 1386 into t, which is 80. Now, is there any, I mean, the way these numbers are given, you can see. 1 by 2000. Yes, yes. So, if you remove this decimal place and multiply with 10 is for minus 3, you will see that this is 2 times and then this becomes 40. So, you will get minus of 4 into 10 raise to the power minus 2. So, n will come out to be n naught times e to the power minus of 0.04. Getting it? So, this is a number of nucleus that are remaining and what we have to find? We have to find fraction of, fraction that is decayed. Okay? So, decayed will be what? n naught minus n. Fine? So, this will be 1 minus e to the power minus of 0.04 into n naught divided by n naught. Fine? So, once you simplify this, you will be getting it as 0.04. Okay? This is a fraction. Once you multiply it with 100, you will get percentage that is 4. Where you guys were getting it wrong? Calculate it. Calculate it. 0.004. So, how can you do that? Oh, you, I think you will be getting lock tables, right? Sir, we have calculators now. You are not allowed to use calculators in exams. So, you should get used to having, I mean using the lock tables. Sir, for advance we have a scientific calculator. Are you sure? Because last time they were not allowed to. There was a rumour that they are getting it, but they did not. Anyways, let me confirm this calculation. Yeah, it comes out to be 0.04. That's correct. So, you have used calculator in the wrong way. I do not understand what you are saying. Okay, guys. So, I mean a lot of things to learn. This is a question that came in 2011. Okay. That time I think there was no J advance that point in time. Anyways, a silver sphere, there is a silver sphere of radius 1 centimeter. It's a silver sphere. Oh, sorry, sorry. You haven't done that dual nature, right? Why for that? Instead of that, please do this. This also came in 2011. Activity of freshly prepared radioactive sample is 10 raise to power, 10 disintegrations per second. This is activity of freshly prepared radioactive sample. Fine. This is equation number one. The mean life T average is 10 raise to power 9 seconds. Okay. The mass of atom, mass of an atom of this radioisotope, mass of atom is given as 10 raise to power minus 25 kgs. Okay. You need to find the mass of the radioactive sample. How many grams of radioactive sample you have? So, could you repeat the question once? The activity of a radioactive sample, the entire sample is 10 raise to power 10 per second. Okay. The average life of this radioactive sample is given 10 raise to power 9 seconds. Okay. Mass of one atom is 10 raise to power minus 25 kgs. What is the mass of entire sample? Should I do it? One second. Sir, is it 10 to the power minus 6 kgs? So, that's like one microgram of one micro kgs. Don't come under too much pressure of your school exams. Okay. Yes, that's correct. 10 raise to power minus 6 kgs. I think this is straightforward. Ramcharan, you got it? Sir, almost. Okay. Who is the new one? Sir, doing it. See, dn by dt is nothing but lambda times n. dn by dt is directly given, which is 10 raise to power 10 per second. Fine. And lambda, you can get from t average. t average is 1 by lambda. So, lambda is 1 by t average, which is 10 raise to power minus 9. This into n is equal to 10 raise to power 10. So, number of nucleases that are there, 10 raise to power 19. Okay. Now, you know that 6.023 into 10 raise to power 23. These many nucleases are there. Oh, sorry. It's not molar mass that is given. It's mass of atom directly given. So, total mass will be equal to number of atoms which is equal to number of nucleases. That is 10 raise to power 19 multiplied by 10 raise to power minus 25. So, it comes out to be 10 raise to power minus 6 kg or 1 milligram or 1 micro kg. Fine. These are your latest J advance questions. So, you see that you will probably learn a lot more from the previous, like when 1990s and beginning of the millennium, those times questions were coming, which were having multiple concepts in a question. So, if you solve those, you will gain lot more clarity. So, don't miss out on the older question thinking that those are very, very old questions. So, let me do the latest ones. Fine. Next question, write down an alpha particle and a proton. Alpha particle and a proton, they both are accelerated from rest by a potential difference of 100 volts. Both are accelerated by 100 volts. After this, their deep Broglie wavelengths are lambda alpha and lambda beta. Sorry, lambda p. Okay. You need to find out ratio of lambda p with lambda alpha to the nearest integer. Okay. How much this is equal to? So, 2. No. So, is it 1? No. Okay. What is the difference between alpha and proton? Charge of alpha is? 2 times the charge of proton. Okay. So, the kinetic energy of alpha, let's say this is K alpha. It will be 2 times of kinetic energy of proton. Does all of you agree? Yes. Same potential difference. Suppose potential difference is V and the charge is Q. So, the kinetic energy gain will be Q into V. So, the charge of alpha is 2 times the charge of proton. That is the reason why the alpha will acquire 2 times the kinetic energy than the proton. So, Q into V is the kinetic energy. All of you understand this, right? Yes, sir. And mass of alpha is approximately 4 times the mass of proton. Can I say that? Yes, sir. Okay. Now, deeply wavelength is what? H by P. Sir, then is it root 2? No. You have to give me an integer as answer. Fine. Momentum can be written in terms of kinetic energy like this, 2 M into K. Fine. So, when I talk about proton, it will be mass of proton, kinetic energy of proton. And when I talk about alpha, have you done it like this only? Sir, I forgot about kinetic energy. You forgot about what? The kinetic energy question. What is the energy conservation and then from the ratio from there? See, the thing is, here, directly the hint is given, you know, the deeply wavelengths are lambda A and lambda B. And you know that deeply wavelength depends on the momentum. And momentum has a relation with kinetic energy. And kinetic energy depends on charge and potential difference. Because it's a very common way of accelerating, you know, a subatomic particle or any smaller particle just have to pass through a potential difference. So, you will gain kinetic energy and depending on kinetic energy, you will get the momentum also, like this. Okay. So, lambda B by lambda alpha is under root of mass of alpha, kinetic energy of alpha divided by mass of proton into kinetic energy of proton. Fine. This will be equal to what? Mass of alpha is 4 times mass of proton and kinetic energy of alpha is 2 times the kinetic energy of proton. So, under root 8 you get and the nearest integer is 3. Okay. Fine. So, I will quickly introduce another question and let's see whether we can do it within our time limits. Otherwise, we'll take it as a homework also. This is a passage-based question. So, when you write J advanced, you will have passage-based question also. Passage is given and it's like a reading comprehension basically. The key feature, I am reading the passage, okay. So, listen carefully. The key feature of Bohr's theory of spectrum of hydrogen atom is quantization of angular momentum when electron is revolving around a proton. So, it is stating the obvious thing, okay, which you already know. We will extend this to a general rotational motion. You are going to extend this quantization that angular momentum is quantized to rotational motion also now. Fine. Rotational motion to find the quantized rotational energy of diatomic molecule. So, when you find the rotational energy of diatomic molecule, you are assuming that Bohr's model of quantization of angular momentum is valid here also. Okay. Assume diatomic molecule to be rigid. For example, carbon monoxide, okay. Assume that there is a rod which connects carbon and oxygen. Treat carbon and oxygen as if two point masses are there. Are you getting it? All of you? Yes. Fine. Now, the rule to be applied is Bohr's quantization condition. Again, it is stating the same thing. Now, solve this question first. A diatomic molecule has moment of inertia i. Moment of inertia is given. Okay. By Bohr's quantization condition, you need to find out its rotational energy. Find out its rotational energy in nth level. Okay. I will just write down the options which are there. You guys can start solving it. The Bohr's model which says angular momentum is quantized is valid here also. What is the rotational energy in the nth level? So, d. D. Ramcharan, Kondanya. Yes, that's correct. Are you guys stuck? Ramcharan, Kondanya. What should I wait? Sir, do answer. Okay. So, see angular momentum for a particle is mvr. Okay. For this condition where carbon oxygen, they are treated like a rigid body. Okay. Don't write mvr. It's l. Okay. So, l is nh by 2 pi. Fine. And its rotational energy should be what? Half i omega square. Now, you can write this rotational energy in terms of l. How? Half i omega whole square divided by i. Now, i omega is angular momentum only. So, this is l square divided by 2i. Fine. Now, substitute value of l over here. You get the option d. Fine. Yes. Okay. Now, the next part of this same comprehension, the second question of this. It is found that, it is found that excitation frequency from ground to the first excited state of rotation. So, from ground, let's say from n equal to 1 to n equal to 2. Excitation frequency is close to 4 by pi into 10 raised to the power 11 hertz. Okay. The movement of inertia of CO molecule i about its center of mass is how much? Okay. Take h to be equal to 2 pi into 10 raised to the power minus 34. Okay. This much SI units. The options are 2.76. Do you guys start doing it? So, what is excitation frequency? See, I'll read the question again. It is found that excitation frequency from ground to the first excited state of the rotation of CO molecule is close to this mu, which is written. The movement of inertia of CO molecule is what? Excitation frequency is the frequency of a photon which excites it from n equal to 1 to n equal to 2. If you want to hear that. Any idea? How will you approach this question? So, doing it so on second. Yes, sir. So, the energy which is released in the transition is equal to the rotation energy? Yeah. The change in rotation energy. Exactly. So, rotation energy you got as a function of n, right? So, you find rotation energy at n equal to 2 and rotation energy at n equal to 1. So, active as a difference will be equal to H mu and from there you will get the value of 5. Fine. You can do it. That's D, right? It's D. Pb, Bombay. Bombay. Yes, that's correct. Anyways, I'll quickly tell you the third question which you can do it at home and message me your answer. In a CO molecule, the distance between carbon whose mass is 12 Amu, carbon atom mass is 12 Amu and oxygen atom mass is 16 Amu. These two masses are given. Atoms mass where 1 Amu is 5 by 3 into 10 raise to power minus 27 Kg. Okay. You need to find distance between carbon and oxygen atom. Fine. Can you quickly tell me how you will approach this? Just, I mean, talk about it. You don't need to solve it right now. So, I think it has to do with gravitational potential energy. No. See, all the questions in reading comprehension, they are usually linked. Like question number two was linked to one. Question number three will have to be linked. I mean, usually. So, can you find any linkage? I'll give you a hint. Moment of inertia is given as if two masses are there. Okay. Moment of inertia about center of mass is this, which you have just calculated. Fine. So, this is the distance r1 and that is a distance r2. Then what? m1 r1 square plus m2 r2 square. This is the moment of inertia. Okay. And since it is a center of mass, m1 r1 will be equal to m2 r2. Okay. Assuming center of mass to be at the origin. Okay. So, just try this your own and message me the final answer. Okay. So, I think you guys are fine up to mains level, but advanced level requires, it doesn't require a lot of practice, but what it requires is you have to open up your mind. As in, you should not think in a constrained manner where this chapter means only this chapter's question and you know, type of question. So, just don't even have that thought in your mind. So, approach a question with open mind. I mean, that's the only feedback I can give you. Right. So, do one thing. I have sent you a lecture on this thing on dual nature of radiation matter. Okay. In Kormangala batch. I think Indranagar batch, I have taken this class and it was online class only. So, I've sent you that particular video on YouTube. So, make sure Kormangala guys, you watch it and we'll focus next class.