The average life T and the decay constant $\mathrm{\lambda }$ of a radioactive nucleus are related as 

(1) $\mathrm{T\lambda }=1$               

(2) $\mathrm{T}=\frac{0.693}{\mathrm{\lambda }}$

(3) $\frac{\mathrm{T}}{\mathrm{\lambda }}=1$               

(4) $\mathrm{T}=\frac{\mathrm{c}}{\mathrm{\lambda }}$

If T is the half life of a radioactive material, then the fraction that would remain after a time $\frac{\mathrm{T}}{2}$ is 
(1) $\frac{1}{2}$             

(2) $\frac{3}{4}$
(3) $\frac{1}{\sqrt{2}}$           

(4) $\frac{\sqrt{2}-1}{\sqrt{2}}$

Which of the following is in the increasing order for penetrating power 

(1) $\mathrm{\alpha },\mathrm{\beta },\mathrm{\gamma }$               

(2) $\mathrm{\beta },\mathrm{\alpha },\mathrm{\gamma }$

(3) $\mathrm{\gamma },\mathrm{\alpha },\mathrm{\beta }$               

(4) $\mathrm{\gamma },\mathrm{\beta },\mathrm{\alpha }$

The half life of a radioactive element which has only $\frac{1}{32}$ of its original mass left after a lapse of 60 days is

(1) 12 days                 

(2) 32 days

(3) 60 days                 

(4) 64 days

The half-life of ${\mathrm{Bi}}^{210}$ is 5 days. What time is taken by (7/8)th part of the sample to decay 

(1) 3.4 days               

(2) 10 days

(3) 15 days               

(4) 20 days

Radioactivity is

(1) Irreversible process             

(2) Self disintegration process

(3) Spontaneous process           

(4) All of the above

Half life of radioactive element depends upon

(1) Amount of element present 

(2) Temperature

(3) Pressure

(4) Nature of element

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