Nucleus produced due to $\mathrm{\alpha }$-decay of the nucleus ${}_{\mathrm{Z}}{}^{\mathrm{A}}\mathrm{X}$ is

(1) ${}_{\mathrm{Z}+2}{}^{\mathrm{A}+4}\mathrm{Y}$                     

(2) ${}_{\mathrm{Z}}{}^{\mathrm{A}}\mathrm{Y}$

(3) ${}_{\mathrm{Z}-2}{}^{\mathrm{A}-4}\mathrm{Y}$                    

(4) ${}_{\mathrm{Z}-4}{}^{\mathrm{A}-2}\mathrm{Y}$

A radioactive material has an initial amount 16 gm. After 120 days it reduces to 1 gm, then the half-life of radioactive material is 

(1) 60 days             

(2) 30 days

(3) 40 days             

(4) 240 days

If a radioactive substance reduces to $\frac{1}{16}$ of its original mass in 40 days, what is its half-life 

(1) 10 days           

(2) 20 days

(3) 40 days           

(4) None of these

The activity of a sample of a radioactive material is ${\mathrm{A}}_1$, at time ${\mathrm{t}}_1$ and ${\mathrm{A}}_2$ at time ${\mathrm{t}}_2$ (${\mathrm{t}}_2$>${\mathrm{t}}_1$). If its mean life T, then 

(1) ${\mathrm{A}}_1{\mathrm{t}}_1={\mathrm{A}}_2{\mathrm{t}}_2$           

(2) ${\mathrm{A}}_1-{\mathrm{A}}_2={\mathrm{t}}_2-{\mathrm{t}}_1$
(3) ${\mathrm{A}}_2={\mathrm{A}}_1{\mathrm{e}}^{\left({\mathrm{t}}_1-{\mathrm{t}}_2\right)/\mathrm{T}}$   

(4) ${\mathrm{A}}_2={\mathrm{A}}_1{\mathrm{e}}^{\left({\mathrm{t}}_1/{\mathrm{t}}_2\right)\mathrm{T}}$

A radioactive nucleus with Z protons and N neutrons emits an $\mathrm{\alpha }$-particle, 2$\mathrm{\beta }$-particles and 2 gamma rays. The number of protons and neutrons in the nucleus left after the decay respectively, are 

(1) Z – 3, N – 1                 

(2) Z – 2, N – 2

(3) Z – 1, N – 3                 

(4) Z, N – 4

The S.I. unit of radioactivity is 

(1) Roentgen         

(2) Rutherford

(3) Curie               

(4) Becqueral

The half-life of a radioactive substance against $\mathrm{\alpha }$-decay is $1.2\times {10}^7$ s. What is the decay rate for $4\times {10}^{15}$ atoms of the substance

(1) $4.6\times {10}^{12}<mspace\; width="1em"></mspace>\mathrm{atoms}/\mathrm{s}$         

(2) $2.3\times {10}^{11}<mspace\; width="1em"></mspace>\mathrm{atoms}/\mathrm{s}$

(3) $4.6\times {10}^{10}<mspace\; width="1em"></mspace>\mathrm{atoms}/\mathrm{s}$          

(4) $2.3\times {10}^8<mspace\; width="1em"></mspace>\mathrm{atoms}/\mathrm{s}$

In a sample of radioactive material, what percentage of the initial number of active nuclei will decay during one mean life 

(1) 69.3%           

(2) 63%

(3) 50%               

(4) 37%

99% of a radioactive element will decay between

(1) 6 and 7 half lives             

(2) 7 and 8 half lives

(3) 8 and 9 half lives             

(4) 9 half lives