The half-life of a radioactive substance is 40 years. How long will it take to reduce to one fourth of its original amount and what is the value of decay constant 

(1) 40 year, 0.9173/year           

(2) 90 year, 9.017/year

(3) 80 year, 0.0173 year           

(4) None of these

A radioactive material has a half life of 10 days. What fraction of the material would remain after 30 days

(1) 0.5               

(2) 0.25

(3) 0.125           

(4) 0.33

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