Two EAMCET Questions from Nuclear Physics

The following MCQ which appeared in EAMCET 2005 question paper highlights the law of conservation of momentum as applied to nuclear processes:

A nucleus of mass 218 amu in free state decays to emit an α-particle. Kinetic energy of the α-particle emitted is 6.7 MeV. The recoil energy (in MeV) of the daughter nucleus is

(a) 1

(b) 0.5

(c) 0.25

(d) 0.125

The kinetic energy (K) is given by

K = p²/2m where p is the momentum and m is the mass. The recoil momentum of the daughter nucleus is equal and opposite to the momentum of the α-particle.

We have p²/(2×4 amu) = 6.7 MeV, since the mass of the α-particle is 4 amu.

[You need not convert amu into kilogram and energy into joule and waste your time. You may imagine that p has proper unit to get the energy in MeV]

In the case of the daughter nucleus (of mass 218 – 4 = 214 amu), we have

p²/(2×214 amu) = K, whetre K is the recoil energy of the daughter (in MeV).

From the above two equations we obtain K = 0.125 MeV.

The following MCQ appeared in EAMCET 2000 question paper:

In a nuclear reactor using U²³⁵ as fuel the power output is 4.8 mega watts. The number of fissions per second is (energy released per fission of U²³⁵ = 200 MeV).

(a) 1.5×10¹⁷

(b) 3×10¹⁹

(c) 1.5×10²⁵

(d) 3×10²⁵

This is a very simple question. The energy produced per second is 4.8×10⁶ joule. Since 1 electron volt is 1.6×10^–19 joule, 200 MeV = 200×10⁶×1.6×10^–19 joule.

Therefore, the number of fissions per second = (4.8×10⁶)/(200×10⁶×1.6×10^–19) = 1.5×10^17.

You can find all related posts on this site by clicking on the label ‘nuclear physics’ below this post.

The Atomic Bomb – A Surprise Question

When I thought of posting a few questions on nuclear fission, a funny incident came to my mind. In the Physics Department we used to conduct ‘surprise colloquium’ for the benefit of our post graduate students. Without giving any prior information, three or four teachers would go to the class with bits of paper on which different topics were written. The paper bits (contained in a small box) would be shuffled and the students asked one by one to pick a bit at random. After drawing a paper bit the student was required to think of the topic written on the paper bit for a couple of minutes and then start talking on the topic. The maximum time allowed for the talk was five minutes. This was followed by questions by students and teachers and answer by the ‘victim’, for few more minutes.

During one such ‘surprise colloquium’ one of the students picked out a paper bit carrying the topic nuclear fission. As usual, he thought of the topic for a while and started presenting the details such as fissionable material, critical mass, chain reaction, Einstein’s mass-energy relation, energy released in fission, moderators and control rods in nuclear reactors and the uncontrolled chain reaction in the atomic bomb. After the torrent of words for well over five minutes, it was question time when one of the listeners (a close friend of the speaker) raised a question:

“We know that the critical mass is only of the order of kilograms. The earth contains tons and tons of fissionable U²³⁵. Yet the earth does not explode. Why?”

The speaker thought for a while and to the surprise of all of us retorted: “Do you know?”

The entire class burst into laughter and the students and the teachers enjoyed the day’s ‘surprise colloquium’ very much…

Most of you know the answer to the above question. You require the fissionable material in a concentrated form, with mass greater than the critical mass, so that the neutrons produced by the fission are able to produce further fissions in neighbouring nuclei. Then only a sustained chain reaction is possible.