## Wednesday, June 26, 2013

### Questions on Atomic Physics Including JEE (Advanced) 2013 Questions

“Happiness comes when your work and words are of benefit to others.”
– Buddha

Today we shall discuss a few multiple choice questions on atomic physics. Questions in this section are simple and interesting. You can work out most of the questions in this section without consuming much time and hence you will be justified in giving some preference to them. Here are the questions with their solution:

(1) An electron and a positron moving along a straight line in opposite directions with equal speeds suffer a head-on collision and get annihilated, producing two photons. Along which directions will the photons travel?

(a) Along straight lines at right angles

(b) Along straight lines inclined at 45 º

(c) Along straight lines inclined at 120 º

(d) Along a straight line in opposite directions

(e) Along straight lines arbitrarily oriented

The net momentum of the system consisting of an electron and a positron moving with the same speed in opposite directions is equal to zero since the electron and the positron have the same mass. Therefore, the net momentum of the products produced in the collision process must be zero in accordance with the law of conservation of momentum. Cancellation of the momenta of the photons (for achieving the condition of zero net momentum) is possible only if the photons travel along a straight line in opposite directions [Option (d)].

(2) Suppose the wave length of one of the photons produced in the pair annihilation process considered in the above question is λ. The wave length of the other photon is

(a) λ

(b) 2 λ

(c) 3 λ

(d) an integral multiple of λ

(e) any thing, which can not be theoretically predicted.

Since the net momentum of the system is zero, the photons must possess equal and opposite momenta. Momentum p of a photon is related to its energy E by

p = E/c where c is the speed of light in free space.

The photons generated must therefore be of the same energy. In other words their wave lengths must be the same [Option (a)].

The following single correct answer type multiple choice question was included in the JEE (Advanced) 2013 question paper:

(3) A pulse of light of duration 100 ns is completely absorbed by a small object initially at rest. Power of the pulse is 30 mW and the speed of light is 3×108 ms–1. The final momentum of the object is

(a) 0.3×10–17 kg ms–1

(b) 1×10–17 kg ms–1

(c) 3×10–17 kg ms–1

(d) 9×10–17 kg ms–1

Since the light pulse is completely absorbed by the object, the entire momentum of the pulse is transferred to the object. If E is the energy of the pulse, the momentum p is given by

p =  E/c where c is the speed of light in free space.

But E = Pt where P is the power and t is the duration of the pulse.

Therefore, we have

p = Pt/c = (30×10–3)×(100×10–9) /( 3×108) = 1×10–17 kg ms–1

The following single digit integer answer type question (in which the answer is an integer ranging from 0 to 9) also was included in the JEE (Advanced) 2013 question paper:

(4) The work functions of silver and sodium are 4.6 and 3.2 eV respectively. The ratio of the slope of the stopping potential versus frequency plot for silver to that of sodium is:

Ans : ?

The maximum kinetic energy KEmax of the photo electron is given by

KEmax = hνφ where h is Planck’s constant, ν is the frequency of the incident radiation and φ is the work function of the photo emitting surface.

If the stopping potential is V, we have

KEmax = eV where e is the electronic charge.

Therefore, eV = hνφ from which

V = (h/e)νφ/e

The above equation shows that if the stopping potebtial V is plotted against the frequency ν, a straight line graph of slope h/e is obtained.

Since h/e is a constant, the slope is the same for all photo emitters. Therefore, the  ratio of  slopes = 1.

Thus Ans. = 1

You will find some useful multiple choice questions from atomic physics and nuclear physics as well as here.