The activity of a sample of a radioactive material is ${\mathrm{A}}_1$, at time ${\mathrm{t}}_1$ and ${\mathrm{A}}_2$ at time ${\mathrm{t}}_2$ (${\mathrm{t}}_2$>${\mathrm{t}}_1$). If its mean life T, then 

(1) ${\mathrm{A}}_1{\mathrm{t}}_1={\mathrm{A}}_2{\mathrm{t}}_2$           

(2) ${\mathrm{A}}_1-{\mathrm{A}}_2={\mathrm{t}}_2-{\mathrm{t}}_1$
(3) ${\mathrm{A}}_2={\mathrm{A}}_1{\mathrm{e}}^{\left({\mathrm{t}}_1-{\mathrm{t}}_2\right)/\mathrm{T}}$   

(4) ${\mathrm{A}}_2={\mathrm{A}}_1{\mathrm{e}}^{\left({\mathrm{t}}_1/{\mathrm{t}}_2\right)\mathrm{T}}$

Nucleus produced due to $\mathrm{\alpha }$-decay of the nucleus ${}_{\mathrm{Z}}{}^{\mathrm{A}}\mathrm{X}$ is

(1) ${}_{\mathrm{Z}+2}{}^{\mathrm{A}+4}\mathrm{Y}$                     

(2) ${}_{\mathrm{Z}}{}^{\mathrm{A}}\mathrm{Y}$

(3) ${}_{\mathrm{Z}-2}{}^{\mathrm{A}-4}\mathrm{Y}$                    

(4) ${}_{\mathrm{Z}-4}{}^{\mathrm{A}-2}\mathrm{Y}$

Which of the following processes represents a gamma-decay

(1) ${}_{\mathrm{Z}}{}^{\mathrm{A}}\mathrm{X}+\mathrm{\gamma }\to {}_{\mathrm{Z}-1}{}^{\mathrm{A}}\mathrm{X}+\mathrm{a}+\mathrm{b}$ 

(2) ${}_{\mathrm{Z}}{}^{\mathrm{A}}\mathrm{X}+{}_0{}^1\mathrm{n}\to {}_{\mathrm{Z}-2}{}^{\mathrm{A}-3}\mathrm{X}+\mathrm{c}$

(3) ${}_{\mathrm{Z}}{}^{\mathrm{A}}\mathrm{X}\to {}_{\mathrm{Z}}{}^{\mathrm{A}}\mathrm{X}+\mathrm{f}$

(4) ${}_{\mathrm{Z}}{}^{\mathrm{A}}\mathrm{X}+{\mathrm{e}}^{-1 }\to {}_{\mathrm{Z}-1}{}^{\mathrm{A}}\mathrm{X}+\mathrm{g}$

The half-life of ${}_{215}\mathrm{At}$ is 100 $\mathrm{\mu s}$. The time taken for the radioactivity of a sample of ${}_{215}\mathrm{At}$ to decay to 1/16th of its initial value is 

(1) 400 $\mathrm{\mu s}$               

(2) 6.3 $\mathrm{\mu s}$ 

(3) 40 $\mathrm{\mu s}$                 

(4) 300 $\mathrm{\mu s}$

The half-life of a radioactive substance is 48 hours. How much time will it take to disintegrate to its $\frac{1}{16}$th part

(1) 12 h             

(2) 16 h

(3) 48 h             

(4) 192 h

A radioactive substance has an average life of 5 hours. In a time of 5 hours 

(1) Half of the active nuclei decay

(2) Less than half of the active nuclei decay

(3) More than half of the active nuclei decay

(4) All active nuclei decay

Which of the following radiations has the least wavelength

(1) X-rays             

(2) $\mathrm{\gamma }$-rays

(3) $\mathrm{\beta }$-rays             

(4) $\mathrm{\alpha }$-rays

A radioactive sample at any instant has its disintegration rate 5000 disintegration per minute. After 5 minutes, the rate is 1250 disintegrations per minute. Then, the decay constant (per minute) is 

(1) 0.8 In 2               

(2) 0.4 In 2

(3) 0.2 In 2               

(4) 0.1 In 2

Radioactive nuclei that are injected into a patient collect at certain sites within its body, undergoing radioactive decay and emitting electromagnetic radiation. These radiations can then be recorded by a detector. This procedure provides an important diagnostic tool called 

(1) Gamma camera

(2) CAT scan

(3) Radiotracer technique

(4) Gamma ray spectroscopy

A radioactive decay chain starts from ${}_{93}{}^{237}\mathrm{Np}$ and produces ${}_{90}{}^{229}\mathrm{Th}$ by successive emissions. The emitted particles can be 

(1) Two $\mathrm{\alpha }$-particles and one $\mathrm{\beta }$-particle

(2) Three ${\mathrm{\beta }}^{+}$ particles

(3) One $\mathrm{\alpha }$ particle and two ${\mathrm{\beta }}^{+}$ particles

(4) One $\mathrm{\alpha }$ particle and two ${\mathrm{\beta }}^{-}$ particles