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

The half life of radioactive Radon is 3.8 days. The time at the end of which 1/20 th of the Radon sample will remain undecayed is
(Given ${\log }_{10}\mathrm{e}=0.4343$) 
(a) 3.8 days               (b) 16.5 days
(c) 33 days                (d) 76 days

If 10% of a radioactive material decays in 5 days, then the amount of original material left after 20 days is approximately
(1) 60%             

(2) 65%

(3) 70%             

(4) 75%

A radioactive isotope X with a half-life of $1.37\times {10}^9$ years decays to Y which is stable. A sample of rock from the moon was found to contain both the elements X and Y which were in the ratio of 1 : 7. The age of the rock is
(a) $1.96\times {10}^8$ years         (b) $3.85\times {10}^9$ years
(c) $4.11\times {10}^9$years          (d) $9.59\times {10}^9$ years

From a newly formed radioactive substance (Half-life 2 hours), the intensity of radiation is 64 times the permissible safe level. The minimum time after which work can be done safely from this source is:
1. 6 hours           
2. 12 hours
3. 24 hours         
4. 128 hours

The half-life of radium is 1620 years and its atomic weight is 226 kg per kilo mol. The number of atoms that will decay from its 1 gm sample per second will be:

(1) $3.61\times {10}^{10}$    

(2) $3.6\times {10}^{12}$

(3) $3.11\times {10}^{15}$     

(4) $31.1\times {10}^{15}$

(Avogardo's number N = $6.02\times {10}^{26}$ atoms/mol)

A radioactive material decays by simultaneous emission of two particles with respective half lives 1620 and 810 years. The time (in years) after which one- fourth of the material remains is 
(a) 1080         (b) 2430
(c) 3240         (d) 4860

The half life period of a radioactive element X is same as the mean life time of another radioactive element Y. Initially both of them have the same number of atoms. Then

(1) X and Y have the same decay rate initially

(2) X and Y decay at the same rate always

(3) Y will decay at a faster rate than X

(4) X will decay at a faster rate than Y