An artificial radioactive decay series begins with unstable ${}_{94}{}^{241}\mathrm{Pu}$. The stable nuclide obtained after eight α decays and five $\mathrm{\beta }$-decays is 

(1) ${}_{83}{}^{209}\mathrm{Bi}$         

(2) ${}_{82}{}^{209}\mathrm{Pb}$

(3) ${}_{82}{}^{205}\mathrm{Ti}$         

(4) ${}_{82}{}^{201}\mathrm{Hg}$

The activity of a sample is $64\times {10}^{-5}$ Ci. Its half-life is 3 days. The activity will become $5\times {10}^{-6}$ Ci after 

(1) 12 days         

(2) 7 days

(3) 18 days         

(4) 21 days

The half-life of radon is 3.8 days. Three forth of a radon sample decay in

(1) 5.02 days         

(2) 15.2 days

(3) 7.6 days           

(4) 11.4 days

A nucleus of an element ${}_{84}{}^{202}\mathrm{X}$ emits an $\mathrm{\alpha }$-particle first, a $\mathrm{\beta }$-particle next and then a gamma photon. The final nucleus formed has an atomic number 

(1) 200           

(2) 199

(3) 83             

(4) 198

Plutonium decays with a half-life of 24000 years. If the plutonium is stored for 72000 years, then the fraction of plutonium that remains is 

(1) $\frac{1}{2}$          

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

(4) $\frac{1}{8}$

A radioactive substance emits 

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

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

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

(4) All of these

The large scale destruction, that would be caused due to the use of nuclear weapons is called 

(1) Nuclear holocaust

(2) Thermo-nuclear reaction

(3) Nuetron reproduction factor

(4) None of these

A radioactive substance has a half-life of 1 year. The fraction of this material, that would remain after 5 years will be

(1) $\frac{1}{32}$             

(2) $\frac{1}{5}$
(3) $\frac{1}{2}$               

(4) $\frac{4}{5}$

If half-life of a substance is 3.8 days and its quantity is 10.38 gm. Then substance quantity remaining left after 19 days will be 

(1) 0.151 gm             

(2) 0.32 gm

(3) 1.51 gm               

(4) 0.16 gm

Which is the correct expression for half-life

(1) ${\mathrm{t}}_{1/2}=\log 2$                 

(2) ${\mathrm{t}}_{1/2}=\frac{\mathrm{\lambda }}{\log 2}$
(3) ${\mathrm{t}}_{1/2}=\frac{\mathrm{\lambda }}{\log 2}(2.303)$     

(4) ${\mathrm{t}}_{1/2}=\frac{2.303 \log 2}{\mathrm{\lambda }}$