Q 11 :

A nucleus disintegrates into two smaller parts, which have their velocities in the ratio 3 : 2. The ratio of their nuclear sizes will be ${\left(\frac{x}{3}\right)}^{1/3}$. The value of $\text{'}x\text{'}$ is ______.    [2023]

Q 12 :

A nucleus disintegrates into two nuclear parts, in such a way that the ratio of their nuclear sizes is $1:2^{1/3}$. Their respective speeds have a ratio of $n:1$. The value of $n$ is ______.                      [2023]

Q 13 :

If an alpha particle with energy 7.7 MeV is bombarded on a thin gold foil, the closest distance from nucleus it can reach is ______ m 
(Atomic number of gold = 79 and $\frac{1}{4\pi {\epsilon }_0}=9\times {10}^9$ in SI units)    [2026]

• $3.85\times {10}^{-16}$

   

• $2.95\times {10}^{-14}$

   

• $3.85\times {10}^{-14}$

   

• $2.95\times {10}^{-16}$

   

Q 14 :

7.9 MeV $\alpha$-particle scatters from a target material of atomic number 79. From the given data, the estimated diameter of nuclei of the target material is (approximately) _____ m.

$[\frac{1}{4\pi {\epsilon }_0}=9\times {10}^9{\text{\hspace{0.05em}Nm}}^2/{\text{C}}^2\text{ and electron charge }=1.6\times {10}^{-19}\text{\hspace{0.05em}C}]$                      [2026]

• $1.44\times {10}^{-13}$

   

• $2.88\times {10}^{-14}$

   

• $1.69\times {10}^{-12}$

   

• $5.76\times {10}^{-14}$

   

Q 15 :

A nucleus has mass number $\alpha$ and radius $R_{\alpha }$. Another nucleus has mass number $\beta$ and radius $R_{\beta }$. If $\beta =8\alpha$ then $R_{\alpha }/R_{\beta }$ is :   [2026]

• 1

   

• 0.5

   

• 2

   

• 8

   

Q 16 :

Which of the following pair of nuclei are isobars of the element?  [2026]

• ${}_1{}^2\mathrm{H}\text{ and }{}_1{}^3\mathrm{H}$

   

• ${}_{92}{}^{236}\mathrm{U}\text{ and }{}_{92}{}^{238}\mathrm{U}$

   

• ${}_1{}^3\mathrm{H}\text{ and }{}_2{}^3\mathrm{He}$

   

• ${}_{80}{}^{198}\mathrm{Hg}\text{ and }{}_{79}{}^{197}\mathrm{Au}$

   

Q 17 :

The average energy released per fission for the nucleus of ${}_{92}{}^{235}\mathrm{U}$ is 190 MeV. When all the atoms of 47 g pure ${}_{92}{}^{235}\mathrm{U}$ undergo fission process, the energy released is $\alpha \times {10}^{23} \text{MeV}$. The value of $\alpha$ is ______.

(Avogadro Number $=6\times {10}^{23}$ per mole)  [2026]