In the ground state,an element has $13$ electrons in the $M$ shell. The element is

The process requiring absorption of energy is

If $\omega$ is a complex cube root of unity,then $\sin \left\{\left(\omega^{10}+\omega^{23}\right) \pi-\frac{\pi}{4}\right\}$ is equal to

Two small drops of mercury,each of radius $R$,coalesce to form a single large drop. The ratio of the total surface energies before and after the change is

$A$ specific volume of $H_2$ requires $24 \ s$ to diffuse out of a container. The time required by an equal volume of $O_2$ to diffuse out under identical conditions is $..... \ s$.

The natural frequency of an $L-C$ circuit is $1,25,000 \text{ cycles/s}$. Then the capacitor $C$ is replaced by another capacitor with a dielectric medium of dielectric constant $K$. In this case,the frequency decreases by $25 \text{ kHz}$. The value of $K$ is