If we did all things we are capable of, we would literally astound ourselves.

– Thomas A. Edison

## Sunday, March 01, 2009

### All India Pre-Medical/Pre-Dental Entrance Examination (AIPMT) 2008 Questions on Nuclear Physics

Here are two multiple choice questions which appeared in All India Pre-Medical/Pre-Dental Entrance Examination (AIPMT) 2008:

(1) Two radioactive materials X1 and X2 have decay constants 5λ and λ respectively. If initially they have the same number of nuclei then the ratio of the number of nuclei of X1 to that of X2 will be 1/e after a time

(1) λ/2

(2) 1/(4λ)

(3) e/λ

(4) λ

If the initial number of nuclei is N0 we have

N1 = N0e–5λ t and

N2 = N0eλ t where N1 and N2 are the number of nuclei of X1 and X12 at time t.

Therefore N1/N2 = e–4λt

This will be equal to 1/e when t =1/(4λ).

(2) Two nuclei have their mass numbers in the ratio of 1:3. The ratio of their nuclear densities would be

(1) 3:1

(2) (3)1/3:1

(3) 1:1

(4) 1:3

The mass of a nucleus is directly proportional to the number (A) of the nucleons. The volume of the nucleus is (4/3)πR3 where R is the nuclear radius. But, R = R0A where R0 is a constant (equal to 1.1 ×10-15m). So, the volume of the nucleus also is directly proportional to the nucleon number A. Since the density is the ratio of mass to volume, it follows that the density of nuclear matter is independent of the nucleon number A so that the correct option is (c).

You will find some useful multiple choice questions (with solution) on nuclear physics at physicsplus