The decay constant of radium is $4.28\times {10}^{-4}$ per year. Its half life will be 

(1) 2000 years       

(2) 1240 years

(3) 63 years           

(4) 1620 years

Which of the following is not a mode of radioactive decay

(1) Positron emission           

(2) Electron capture

(3) Fusion                         

(4) Alpha decay

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

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