The relationship between disintegration constant $\left[\lambda \right]$ and half-life [T] will be:

1. $\lambda =\frac{{\log }_{10} 2}{T}$ 

2. $\lambda =\frac{{\log }_e 2}{T}$

3. $\lambda =\frac{T}{{\log }_e 2}$   

4. $\lambda =\frac{{\log }_2 e}{T}$

Alpha particles are 

1. 2 free protons

2. helium atoms

3. singly ionized helium atoms

4. doubly ionised helium atoms

A radioactive sample with a half-life of 1 month has the label: 'Activity = 2 microcurie on 1-8-1991'. What would be its activity two months earlier? 

1. 1.0 microcurie       

2. 0.5 microcurie           

3. 4 microcurie             

4. 8 microcurie

If the nuclear force between two protons, two neutrons and between a proton and a neutron is denoted by $F_{pp},$ $F_{nn}$ $and$ $F_{pn}$ respectively, then:

1. $F_{pp}\approx F_{nn}\approx F_{pn}$

2. $F_{pp}\ne F_{nn}$ $and$ $F_{pn}=F_{nn}$

3. $F_{pp}=F_{nn}=F_{pn}$

4. $F_{pp}\ne F_{nn}\ne F_{pn}$

A radioactive element has half-life period 800 yr. After 6400 yr, what fraction will remain? [1989]

1. $\frac{1}{2}$

2. $\frac{1}{16}$ 

3. $\frac{1}{8}$ 

4.$\frac{1}{256}$

If a proton and anti-proton come close to each other and annihilate, how much energy will be released:

1. $1.5\times {10}^{-10} J$           

2. $3\times {10}^{-10} J$         

3. $4.5\times {10}^{-10} J$         

4. None of these

The stable nucleus that has a radius half of the radius of $F{e}^{56}$ is:

1. $L{i}^7$ 

2. $N{a}^{21}$

3. $S^{16}$

4. $C{a}^{40}$

The mass density of a nucleus varies with mass number A as [1992]

1. $A^2$

2. A 

3. Constant 

4. $\frac{1}{A}$

Energy released in the fission of a single ${}_{92}U_{235}$ nucleus is 200 MeV. The fission rate of a ${}_{92}U_{235}$ filled reactor operating at a power level of 5 W is 

1. $1.56\times {10}^{-10} s^{-1}$ 

2. $1.56\times {10}^{11} s^{-1}$

3. $1.56\times {10}^{-16} s^{-1}$   

4. $1.56\times {10}^{-17} s^{-1}$

In one \(\alpha-\)$$ and \(2\beta-\)$emissions:$