At time t = 0, N₁ nuclei of decay constant λ₁ and N₂ nuclei of decay constant λ₂ are mixed. The decay rate of the mixture is:

1. $-N_1{N}_2{e}^{-\left({\lambda }_1+{\lambda }_2\right)t}$ $$

2. $-\left(\frac{N_1}{N_2}\right)$ $e^{{}^{-\left({\lambda }_1+{\lambda }_2\right)t}}$ $$

3. $-\left(N_1{\lambda }_1{e}^{-{\lambda }_{1}t}\right)$ $+$ $N_2{\lambda }_2{e}^{-{\lambda }_{2}t}$ $$

4. $-N_1{\lambda }_1{N}_2{\lambda }_2{e}^{{}^{-\left({\lambda }_1+{\lambda }_2\right)t}}$

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.

The nuclei ${}_{6}C_{13} and {}_{7}N_{14}$ can be described as [1990]

1. isotones

2. isobars 

3. isotopes of carbon

4. isotopes of nitrogen

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. $A_1{t}_1-A_2{t}_2$

What is the radius of iodine atom? (atomic no. 53, mass no. 126) [1988]

1. $2.5\times {10}^{-11} m$

2. $2.5\times {10}^{-9} m$

3. $7\times {10}^{-9} m$

4. $7\times {10}^{-6} m$

Which of the following statements is true for nuclear forces? [1990]

1. They obey the inverse square law of distance.

2. They obey the inverse third power law of distance.

3. They are short range forces.

4. They are equal in strength to electromagnetic forces.

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. $\lambda =\frac{{\log }_2 e}{T}$