Carbon-14 decays with half-life of about 5,800 years. In a sample of bone, the ratio of carbon-14 to carbon-12 is found to be $\frac{1}{4}$ of what it is in free air. This bone may belong to a period about x centuries ago, where x is nearest to 

(1) 2$\times$58                       

(2) 58

(3) 58/2                         

(4) 3$\times$58

In the disintegration series ${}_{92}{}^{238}\mathrm{U}\stackrel{\mathrm{\alpha }}{\to }\mathrm{X}\stackrel{\mathrm{\beta }-}{\to }{}_{\mathrm{Z}}{}^{\mathrm{A}}\mathrm{Y}$ the values of Z and A respectively will be 

(1) 92, 236               

(2) 88, 230

(3) 90, 234               

(4) 91, 234

The particles emitted by radioactive decay are deflected by magnetic field. The particles will be

(1) Protons and $\mathrm{\alpha }$-particles

(2) Electrons, protons and $\mathrm{\alpha }$-particles

(3) Electrons, protons and neutrons

(4) Electrons and $\mathrm{\alpha }$-particles

Half life of a radioactive element is 10 days. The time during which quantity remains 1/10 of initial mass will be

(1) 100 days             

(2) 50 days

(3) 33 days               

(4) 16 days

In the given nuclear reaction A, B, C, D, E represents
${}_{92}{}^{238}\mathrm{U}\stackrel{\mathrm{\alpha }}{\to }{}_{\mathrm{B}}{}^{\mathrm{A}}\mathrm{Th}\stackrel{\mathrm{\beta }}{\to }{}_{\mathrm{D}}{}^{\mathrm{C}}\mathrm{Pa}\stackrel{\mathrm{E}}{\to }{}_{92}{}^{234}\mathrm{U}$

(1) A = 234, B = 90, C = 234, D = 91, E = $\mathrm{\beta }$

(2) A = 234, B = 90, C = 238, D = 94, E =$\mathrm{\alpha }$

(3) A = 238, B = 93, C = 234, D = 91, E = $\mathrm{\beta }$

(4) A = 234, B = 90, C = 234, D = 93, E = $\mathrm{\alpha }$

If half life of a radioactive element is 3 hours, after 9 hours its activity becomes 

(1) 1/9                     

(2) 1/27

(3) 1/6                     

(4) 1/8

At any instant the ratio of the amount of radioactive substances is 2 : 1. If their half lives be respectively 12 and 16 hours, then after two days, what will be the ratio of the substances?

(1) 1 : 1                 

(2) 2 : 1

(3) 1 : 2                 

(4) 1 : 4

Which of the following isotopes is used for the treatment of cancer 

(1) ${\mathrm{K}}^{40}$        

(2) ${\mathrm{Co}}^{60}$

(3) ${\mathrm{Sr}}^{90}$       

(4) ${\mathrm{I}}^{131}$

If half-life of a radioactive atom is 2.3 days, then its decay constant would be 

(1) 0.1           

(2) 0.2

(3) 0.3           

(4) 2.3

A radio isotope has a half life of 75 years. The fraction of the atoms of this material that would decay in 150 years will be

(1) 66.6%               

(2) 85.5%

(3) 62.5%               

(4) 75%