Starting with a sample of pure ${}_{66}\mathrm{Cu}$, $\frac{7}{8}$ of it decays into Zn in 15 min. The corresponding half-life is 

(1) 5 min               

(2) $7\frac{1}{2}$ min
(3) 10 min             

(4) 15 min

A radioactive material has a half-life of 8 years. The activity of the material will decrease to about 1/8 of its original value in 

(1) 256 year           

(2) 128 year

(3) 64 year             

(4) 24 year

A nucleus of mass 218 amu in free state decays to emit an $\mathrm{\alpha }$-particle. Kinetic energy of the $\mathrm{\alpha }$-particle emitted is 6.7 MeV. The recoil energy (in MeV) of the daughter nucleus is

(1) 1.0             

(2) 0.5

(3) 0.25           

(4) 0.125

${\mathrm{C}}^{14}$ has half life 5700 years. At the end of 11400 years, the actual amount left is  

(1) 0.5 of original amount

(2) 0.25 of original amount

(3) 0.125 of original amount

(4) 0.0625 of original amount

Mean life of a radioactive sample is 100 seconds. Then its half life (in minutes) is

(1) 0.693               

(2) 1

(3) ${10}^{-4}$                 

(4) 1.155

${}_{86}{}^{222}\mathrm{A}\to {}_{84}{}^{210}\mathrm{B}$. In this reaction how many $\mathrm{\alpha }$ and $\mathrm{\beta }$ particles are emitted 
(a) 6$\mathrm{\alpha }$, 3$\mathrm{\beta }$          (b) 3$\mathrm{\alpha }$, 4$\mathrm{\beta }$ 
(c) 4$\mathrm{\alpha }$, 3$\mathrm{\beta }$          (d) 3$\mathrm{\alpha }$, 6$\mathrm{\beta }$  

The phenomenon of radioactivity is 
(1) Exothermic change which increases or decreases with temperature

(2) Increases on applied pressure

(3) Nuclear process does not depend on external factors

(4) None of the above

If half life of radium is 77 days. Its decay constant in day will be
(1) $3\times {10}^{-13}$/day           

(2) $9\times {10}^{-3}$/day

(3) $1\times {10}^{-3}$/day             

(4) $6\times {10}^{-3}$/day

Consider two nuclei of the same radioactive nuclide. One of the nuclei was created in a supernova explosion 5 billion years ago. The other was created in a nuclear reactor 5 minutes ago. The probability of decay during the next time is 
(1) Different for each nuclei

(2) Nuclei created in explosion decays first

(3) Nuclei created in the reactor decays first

(4) Independent of the time of creation

An $\mathrm{\alpha }$-particle of 5 MeV energy strikes with a nucleus of uranium at stationary at a scattering angle of 180^o. The nearest distance up to which $\mathrm{\alpha }$-particle reaches the nucleus will be of the order of:
(1) 1 Å               

(2) ${10}^{-10} \mathrm{cm}$ 

(3) ${10}^{-12} \mathrm{cm}$      

(4) ${10}^{-15} \mathrm{cm}$