Q: Two radioactive elements A and B initially have same number of atoms. The half life of A is same as the average life of B. If _A and _B are decay constants of A and B respectively, then choose the cor

It is given that aligned & ( T _1 2 )_ A = ( T _ av )_ B \\ & T _ 1 / 2 = n 2 and T _ av = 1 \\ & n 2 _ A = 1 _ B _ A = _ B n 2 aligned

Question 1

The atomic mass of _6 C ^ 12 is 12.000000 u and that of _6 C ^ 13 is 13.003354 u . The required energy to remove a neutron from _6 C ^ 13 , if mass of neutron is 1.008665 u , will be:

Accepted Answer

_6 C ^ 13 + Energy _6 C ^ 12 + _0 n ^1 Mass defect, m =(12.000000+1.008665)- 13.003354 =-0.00531 u Energyrequired = m 931.5=0.00531 931.5 MeV =4.95 MeV

Question 2

The nucleus having highest binding energy per nucleon is

Accepted Answer

The binding energy per nucleon is practically independent of the atomic number for nuclei of mass number in range 30 A 17^ . So, 26^ Fe ^ 56 has maximum binding energy per nucleon.

Question 3

Two radioactive elements A and B initially have same number of atoms. The half life of A is same as the average life of B. If _A and _B are decay constants of A and B respectively, then choose the cor

Accepted Answer

It is given that aligned & ( T _1 2 )_ A = ( T _ av )_ B \ & T _ 1 / 2 = n 2 and T _ av = 1 \ & n 2 _ A = 1 _ B _ A = _ B n 2 aligned

Question 4

A radio-active material is reduced to 1 / 8 of its original amount in 3 days. If 8 10^ -3 ~kg of the material is left after 5 days. The initial amount of the material is

Accepted Answer

N = N _0 ( 1 2 )^ n N = N _0 8 N _0 8 = N _0 ( 1 2 )^ n ( 1 2 )^3= ( 1 2 )^ n n =3 3 half lives =3 days 1 half life =1 day 5 days =5 half life N = N _0 ( 1 2 )^ n 8 10^ -3 = N _0 ( 1 2 )^5 N_0=2^5 8 10^ -3 =256 gm

Question 5

In a radioactive material the activity at time t_1, is A_1 and at a later time t_2, it is A_2. If the decay constant of the material is , then

Accepted Answer

From radioactive decay law, - d N d t N or - d N d t = N Thus, A=- d N d t or A= N A= N_0 e^ - t Where, A_0= N_0 is the activity of the radioactive material at time, t=0 At time, t_1 A_1=A_0 e^ - t_1 At time, t_2 A_2=A_0 e^ - t_2 On dividing Eq. (ii) by Eq. (iii), we have aligned A_1 A_2 & = e^ - t_1 e^ - t_2 =e^ - (t_1-t_2 ) \ A_1 & =A_2 e^ - (t_1-t_2 ) aligned

Question 6

Three specimens A, B, C of same radioactive element has activities 1 microcurie, 1 rutherford and 1 becquerel respectively. Which specimen has maximum mass?

Accepted Answer

1 becquerel =1 dis / s 1 rutherford =10^ 6 dis / s 1 curie =3.7 10^ 10 dis / s

Nuclear Physics — Previous Year Questions & Solutions