If half life of radium is 77 days. Its decay constant in day will be
(1) $3\times {10}^{-13}$/day           

(2) $9\times {10}^{-3}$/day

(3) $1\times {10}^{-3}$/day             

(4) $6\times {10}^{-3}$/day

Consider two nuclei of the same radioactive nuclide. One of the nuclei was created in a supernova explosion 5 billion years ago. The other was created in a nuclear reactor 5 minutes ago. The probability of decay during the next time is 
(1) Different for each nuclei

(2) Nuclei created in explosion decays first

(3) Nuclei created in the reactor decays first

(4) Independent of the time of creation

An $\mathrm{\alpha }$-particle of 5 MeV energy strikes with a nucleus of uranium at stationary at a scattering angle of 180^o. The nearest distance up to which $\mathrm{\alpha }$-particle reaches the nucleus will be of the order of:
(1) 1 Å               

(2) ${10}^{-10} \mathrm{cm}$ 

(3) ${10}^{-12} \mathrm{cm}$      

(4) ${10}^{-15} \mathrm{cm}$

A neutron with velocity V strikes a stationary deuterium atom. Its kinetic energy changes by a factor of 
(1) $\frac{15}{16}$             

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

(3) $\frac{2}{1}$               

(4) None of these

The sun radiates energy in all directions. The average radiations received on the earth surface from the sun is 1.4 $\mathrm{kilowatt}/{\mathrm{m}}^2$.The average earth- sun distance is $1.5\times {10}^{11}$ metres. The mass lost by the sun per day is
(1 day = 86400 seconds) 
(a) $4.4\times {10}^9 \mathrm{kg}$          (b) $7.6\times {10}^{14} \mathrm{kg}$
(c) $3.8\times {10}^{12} \mathrm{kg}$         (d) $3.8\times {10}^{14} \mathrm{kg}$

The binding energy per nucleon of ${\mathrm{O}}^{16}$ is 7.97 MeV and that of ${\mathrm{O}}^{17}$ is 7.75 MeV. The energy (in MeV) required to remove a neutron from ${\mathrm{O}}^{17}$ is 
(a) 3.52                 (b) 3.64
(c) 4.23                 (d) 7.86

The rest energy of an electron is 0.511 MeV. The electron is accelerated from rest to a velocity 0.5 c. The change in its energy will be
(1) 0.026 MeV           

(2) 0.051 MeV

(3) 0.079 MeV           

(4) 0.105 MeV

For uranium nucleus how does its mass vary with volume

(1) $\mathrm{m}\propto \mathrm{V}$          

(2) $\mathrm{m}\propto 1/\mathrm{V}$

(3) $\mathrm{m}\propto \sqrt{\mathrm{V}}$       

(4) $\mathrm{m}\propto {\mathrm{V}}^2$

In the nuclear fusion reaction ${}_1{}^2\mathrm{H}+{}_1{}^3\mathrm{H}\to {}_2{}^4\mathrm{He}+\mathrm{n}$ given that the repulsive potential energy between the two nuclei is $-7.7\times {10}^{-14} \mathrm{J}$, the temperature at which the gases must be heated to initiate the reaction is nearly
[Boltzmann’s constant $\mathrm{k}=1.38\times {10}^{-23} \mathrm{J}/\mathrm{K}$)
(a)${10}^9 \mathrm{K}$            (b) ${10}^7 \mathrm{K}$
(c) ${10}^5 \mathrm{K}$           (d)  ${10}^3 \mathrm{K}$

A nucleus with mass number 220 initially at rest emits an $\mathrm{\alpha }$-particle. If the Q value of the reaction is 5.5 MeV, calculate the kinetic energy of the $\mathrm{\alpha }$-particle

(1) 4.4 MeV             

(2) 5.4 MeV

(3) 5.6 MeV             

(4) 6.5 MeV