The radius of a nucleus is given by $r = r_0 A^{1/3}$,where $r_0 = 1.3 \times 10^{-15} \, m$ and $A$ is the mass number of the nucleus. The lead nucleus has $A = 206$. The electrostatic force between two protons at diametrically opposite points in this nucleus is approximately ................ $N$.

Given below are three schematic graphs of potential energy $V(r)$ versus distance $r$ for three atomic particles: electron $(e^{-})$,proton $(p^{+})$,and neutron $(n)$,in the presence of a nucleus at the origin $O$. The radius of the nucleus is $r_0$. The scale on the $V$-axis may not be the same for all figures. The correct pairing of each graph with the corresponding atomic particle is

When a $U^{238}$ nucleus,initially at rest,decays by emitting an alpha particle with speed $u$,what will be the recoil velocity of the residual nucleus?

The mass of a neutron is approximately the same as that of:

The radius $R$ of a nucleus of mass number $A$ can be estimated by the formula $R = (1.3 \times 10^{-15}) A^{1/3} \; m$. It follows that the mass density of a nucleus is of the order of $(M_{\text{prot}} \cong M_{\text{neut}} = 1.67 \times 10^{-27} \; kg)$.

An atom of mass number $15$ and atomic number $7$ captures an $\alpha$-particle and then emits a proton. The mass number and atomic number of the resulting product will respectively be