A radioactive decay chain starts from ${}_{93}{}^{237}\mathrm{Np}$ and produces ${}_{90}{}^{229}\mathrm{Th}$ by successive emissions. The emitted particles can be 

(1) Two $\mathrm{\alpha }$-particles and one $\mathrm{\beta }$-particle

(2) Three ${\mathrm{\beta }}^{+}$ particles

(3) One $\mathrm{\alpha }$ particle and two ${\mathrm{\beta }}^{+}$ particles

(4) One $\mathrm{\alpha }$ particle and two ${\mathrm{\beta }}^{-}$ particles

The half-life of a sample of a radioactive substance is 1 hour. If $8\times {10}^{10}$ atoms are present at t = 0, then the number of atoms decayed in the duration t = 2 hour to t = 4 hour will be

(1) $2\times {10}^{10}$         

(2) $1.5\times {10}^{10}$

(3) Zero               

(4) Infinity

Carbon dating is best suited for determining the age of fossils if their age in years is of the order of 
(1) ${10}^3$            

(2) ${10}^4$

(3) ${10}^5$             

(4) ${10}^6$

A count rate meter shows a count of 240 per minute from a given radioactive source. One hour later the meter shows a count rate of 30 per minute. The half-life of the source is

(1) 120 min                   

(2) 80 min

(3) 30 min                     

(4) 20 min

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