In the following nuclear reaction $_{12}Mg^{24} + _{2}He^{4} \to _{14}Si^{X} + _{0}n^{1}$,the value of $X$ is:

Given below are two statements $:$ one is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$.
Assertion $(A) :$ The density of the copper $\left({ }_{29}^{64} Cu \right)$ nucleus is greater than that of the carbon $\left({ }_6^{12} C \right)$ nucleus.
Reason $(R) :$ The nucleus of mass number $A$ has a radius proportional to $A^{1/3}$.
In the light of the above statements,choose the most appropriate answer from the options given below.

Pick out the correct statement from the following.

$A$ radioactive nucleus of mass $M$ emits a photon of frequency $f$ and the nucleus recoils. The recoil energy will be

If the nuclear force between two protons,two neutrons,and between a proton and a neutron is denoted by $F_{pp}$,$F_{nn}$,and $F_{pn}$ respectively,then:

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