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

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.$\frac{1}{256}$

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. $\gamma , \beta , \alpha$

An observer A sees an asteroid with a radioactive element moving by at a speed = 0.3 c and measures the radioactivity decay time to be $T_A$. Another observer B is moving with the asteroid and measures its decay time as $T_B$. Then $T_A$ and $T_B$ are related as below [VITEEE 2008]

1. $T_B$ < $T_A$

2. $T_B$ = $T_A$

3. $T_B$ > $T_A$

4. Either 1 or 3 depending on whether the asteroid is approaching or moving away from A.

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

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