In the Bohr model of the hydrogen atom, let R, v and E represent the radius of the orbit, the speed of electron and the total energy of the electron respectively. Which of the following quantity is proportional to the quantum number n ?

(1) R/E               

(2) E/v

(3) RE               

(4) vR

If the atom ${}_{100}{}^{257}\mathrm{Fm}$ follows the Bohr model and the radius of ${}_{100}{}^{257}\mathrm{Fm}$ is n times the Bohr radius, then the value of n is:

(1) 100               
(2) 200
(3) 4                   
(4) $\frac{1}{4}$

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

The rest mass of an electron as well as that of positron is 0.51 MeV. When an electron and positron are annihilated, they emit photon of wavelength(s)-

1. 0.012 Å               

2. 0.024 Å

3. 0.012 Å to $\infty$     

4. 0.024 Å to $\infty$

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