Atomic mass number of an element thorium is 232 and its atomic number is 90. The end product of this radioactive element is an isotope of lead (atomic mass 208 and atomic number 82). The number of alpha and beta particles emitted is

 
(1) $\mathrm{\alpha }$=3, $\mathrm{\beta }$ = 3       

(2) $\mathrm{\alpha }$ = 6, $\mathrm{\beta }$ = 4

(3) $\mathrm{\alpha }$=6, $\mathrm{\beta }$=0         

(4) $\mathrm{\alpha }$=4, $\mathrm{\beta }$=6

A sample contains 16 gm of a radioactive material, the half life of which is two days. After 32 days, the amount of radioactive material left in the sample is

(1) Less than 1 mg         

(2) $\frac{1}{4}\mathrm{gm}$ 

(3) $\frac{1}{2}\mathrm{gm}$                       

(4) 1 gm

A radio-isotope has a half- life of 5 years. The fraction of the atoms of this material that would decay in 15 years will be

(1) 1/8             

(2) 2/3

(3) 7/8             

(4) 5/8

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