The binding energies of the nuclei A and B are $E_a and E_b$ respectively. Three atoms of the element B fuse to give one atom of element A and an energy Q is released. Then $E_a, E_b$ 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

Solar energy is due to:

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. $A^{1/3}$

$m_P$ and $m_n$ are masses of proton and neutron respectively. An element of mass m has Z protons and N neutrons, then 

1. $m>Z{m}_p+N{m}_n$

2. $m=Z{m}_p+N{m}_n$

3. $m<Z{m}_p+N{m}_n$

4. m may be greater than, less than or equal to $Z{m}_p+N{m}_n$, depending on the nature of the element.