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. $\lambda =\frac{{\log }_2 e}{T}$

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

1. $\frac{1}{2}$

2. $\frac{1}{16}$ 

3. $\frac{1}{8}$ 

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

If radius of the ${}_{12}{}^{27}Al$ nucleus is taken to be $R_{Al}$, then the radius of ${}_{53}{}^{125}Te$ nucleus is nearly 

1. $\frac{5}{3}{R}_{Al}$ 

2. $\frac{3}{5}{R}_{Al}$ 

3. ${\left(\frac{13}{53}\right)}^{1/3}{R}_{Al}$ 

4. ${\left(\frac{53}{13}\right)}^{1/3}{R}_{Al}$

In a given reaction,

${}_{Z}X_A\to {}_{Z+1}Y_A\to {}_{Z-1}K_{A-4}\to {}_{Z-1}K_{A-4}$

Radioactive radiations are emitted in the sequence of  

1.  $\alpha , \beta , \gamma$ 

2. $\gamma , \alpha , \beta$ 

3. $\beta , \alpha , \gamma$ 

4. $\gamma , \beta , \alpha$

A sample of radioactive element has a mass of 10 g at an instant t = 0. The approximate mass of this element in the sample after two mean lives is [2003]

1. 3.70 g

2. 6.30 g

3. 1.35 g

4. 2.50 g

The mass density of a nucleus varies with mass number A as 

1. $A^2$

2. A 

3. Constant 

4. $\frac{1}{A}$

A nuclear decay is expressed as:
\(_{6}^{11}\mathrm{C}\rightarrow _{5}^{11}\mathrm{B}+\beta^{+}+\mathrm{X}\)
Then the unknown particle \(X\) is:
1. neutron 
2. antineutrino
3. proton 
4. neutrino

The minimum wavelength of X-rays produced by electrons accelerated by a potential difference of V volt is equal to 

1. $\frac{eV}{hc}$ 

2. $\frac{eh}{cV}$ 

3. $\frac{hc}{eV}$ 

4. $\frac{cV}{eh}$

The energy released by the fission of one  uranium atom is 200 MeV. The number of fission per second required to produce 3.2 W of power is (Take, 1 eV = 1.6$\times$${10}^{-19} J$) 

1. ${10}^7$ 

2. ${10}^{10}$ 

3. ${10}^{15}$

4. ${10}^{11}$