The binding energies of the nuclei A and B are $E_a<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>E_b$ respectively. Three atoms of the element B fuse to give one atom of element A and an energy Q is released. Then $E_a,<mspace\; width="1em"></mspace>E_b$ and Q are related as:

1. $E_a-3E_b=Q$ 

2. $3E_b-E_a=Q$

3. $E_a+3E_b=Q$ 

4. $E_b+3E_a=Q$

A free neutron decays into a proton, an electron and:

1. A beta particle.

2. An alpha particle.

3. An antineutrino.

4. A neutrino.

In a radioactive sample the fraction of initial number of radioactive nuclei, which remains undecayed after n mean lives is:

1. $\frac{1}{e^n}$ 

2.  $e^n$   

3. $1-\frac{1}{e^n}$ 

4. ${\left(\frac{1}{e-1}\right)}^n$

The activity of a radioactive sample is measured as 9750 counts/min at t = 0 and as 975 counts/min at t = 5 min. The decay constant is approximately:

1. 0.922/min           

2. 0.691/min         

3. 0.461/min           

4. 0.230/min

Fission of nuclei is possible because the binding energy per nucleon in them [2005]

1. increases with mass number at high mass number

2. decreases with mass number at high mass

3. increases with mass number at low mass numbers

4. decreases with mass number at low mass number

A nucleus ${}_n{}^{m}X$ emits one $\alpha$ and two $\beta -$particles. The resulting nucleus is

1. ${}_n{}^{m-4}X$ 

2. ${}_{n-2}{}^{m-4}X$   

3. ${}_{n-4}{}^{m-4}X$ 

4. None of these

The half-life period of a radioactive substance is 6 h.  If after 24 h, activity is 0.01 $\mu$Ci, what was the initial activity? 

1. 0.04 $\mu$Ci 

2. 0.08 $\mu$Ci

3. 0.24 $\mu$Ci 

4. 0.16 $\mu$Ci

The radius of a nucleus of a mass number A is directly proportional to [MH CET 1999; AMU (En.) 2001; UPSEAT 2004; DUMET 2010]

1. $A^3$ 

2. A 

3. $A^{2/3}$

4. $A^{1/3}$

The radioactivity of a sample is $A_1$ at a time $t_1$ and $A_2$ at time $t_2$.  If the mean life of the specimen is T, the number of atoms that have disintegrated in the time interval of $t_2-t_1$ is:

1. $A_1-A_2$ 

2. $\frac{A_1-A_2}{T}$

3. $\left(A_1-A_2\right)T$

4. $A_1{t}_1-A_2{t}_2$

Three fourth of the active nuclei decay in a radioactive sample in 3/4 s. The half-life of the sample is

1. $\frac{1}{2}<mspace\; width="1em"></mspace>s$ 

2. 1 s   

3. $\frac{3}{8}<mspace\; width="1em"></mspace>s$ 

4. $\frac{3}{4}<mspace\; width="1em"></mspace>s$