Three $\mathrm{\alpha }$-particles and one $\mathrm{\beta }$-particle decaying takes place in series from an isotope ${}_{88}{}^{236}\mathrm{Ra}$. Finally the isotope obtained will be 

(1) ${}_{84}{}^{220}\mathrm{X}$         

(2) ${}_{86}{}^{222}\mathrm{X}$

(3) ${}_{83}{}^{224}\mathrm{X}$         

(4) ${}_{83}{}^{215}\mathrm{X}$

Half life of a radioactive substance is T. The time taken for all the nuclei to disintegrate will be

(1) 2T           

(2) ${\mathrm{T}}^2$

(3) 4T           

(4) Uncertain

The half life of polonium is 140 days. After how many days, 16 gm polonium will be reduced to 1 gm (or 15g will decay) 

(1) 700 days           

(2) 280 days

(3) 560 days           

(4) 420 days

An archaeologist analyses the wood in a prehistoric structure and finds that ${\mathrm{C}}^{14}$(Half life = 5700 years) to ${\mathrm{C}}^{12}$ is only one- fourth of that found in the cells buried plants. The age of the wood is about 

(1) 5700 years               

(2) 2850 years

(3) 11,400 years           

(4) 22,800 years

A radioactive element emits 200 particles per second. After three hours 25 particles per second are emitted. The half life period of element will be
(1) 50 minutes           

(2) 60 minutes

(3) 70 minutes           

(4) 80 minutes

The half life of the isotope ${}_{11}{}^{24}\mathrm{Na}$ is 15 hrs. How much time does it take for $\frac{7}{8}\mathrm{th}$ of a sample of this isotope to decay

(1) 75 hrs               

(2) 65 hrs

(3) 55 hrs               

(4) 45 hrs

If the half life of a radioactive sample is 10 hours,
its mean life is 

(1) 14.4 hours               

(2) 7.2 hours

(3) 20 hours                 

(4) 6.93 hours

If 20 gm of a radioactive substance due to radioactive decay reduces to 10 gm in 4 minutes, then in what time 80 gm of the same substance will reduce to 10 gm 

(1) In 8 minutes             

(2) In 12 minutes

(3) In 16 minutes             

(4) In 20 minutes

16 gm sample of a radioactive element is taken from Bombay to Delhi in 2 hour and it was found that 1 gm of the element remained (undisintegrated). Half life of the element is 

(1) 2 hour         

(2) 1 hour

(3) $\frac{1}{2}$ hour         

(4) $\frac{1}{4}\mathrm{hour}$

Unit of radioactivity is Rutherford. Its value is

(1) $3.7\times {10}^{10}$ disintegrations/sec

(2) $3.7\times {10}^6$ disintegrations/sec

(3) $1.0\times {10}^{10}$disintegrations/sec

(4) $1.0\times {10}^6$ disintegrations/sec