The nuclear radius is given by $R=r_0 A^{1 / 3}$, where $r_0$ is constant and $A$ is the atomic mass number. Then, the nuclear mass density of $U^{238}$ is

For the decay of nucleus, the possible reason which is not true

The increasing order of atomic radii of the following Group $13$ elements is

Assertion $(A):$ Forces acting between proton-protn $\left(f_{p p}\right)$, proton-neutron $\left(f_{p p}\right)$ and neutron-neutron $\left(f_{n n}\right)$ are such that $f_{p p} < f_{p n}=f_{n n}$

Reason $(R):$ Electrostatic force of repulsion between two protons reduces net nuclear forces between them.

$(a)$ Two stable isotopes of lithium $_{3}^{6} L$ and $_{3}^{7} L$ have respective abundances of $7.5 \%$ and $92.5 \% .$ These isotopes have masses $6.01512\; u$ and $7.01600\; u ,$ respectively. Find the atomic mass of lithium.

$(b)$ Boron has two stable isotopes, $_{5}^{10} B$ and $^{11}_{5} B$. Their respective masses are $10.01294 \;u$ and $11.00931\; u$, and the atomic mass of boron is $10.811\; u$. Find the abundances of $_{5}^{10} B$ and $_{5}^{11} B$

$1 a.m.u.$  is equivalent to