A nucleus of atomic mass A and atomic number Z emits $\mathrm{\beta }$-particles. The atomic mass and atomic number of the resulting nucleus are 

(1) A, Z             

(2) A + 1, Z

(3) A, Z + 1       

(4) A-4, Z-2 

Radioactivity was discovered by

(1) Becquerel           

(2) Pierre Curie

(3) Roentgen             

(4) Rutherford

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