Is there any relation between gamma rays and the size of the nucleus?

Question

The wavelength of gamma rays is less than $10^{-11}$ meters but never less than $10^{-14}$ meters. Is this because size of nucleus is $10^{-14}$ meters?

Answer 1

Wavelength $\lambda$ is related energy by $$ E = \frac{hc}{\lambda}.$$

The wavelength range you quote corresponds to energies in the range $0.1 < E < 10$ MeV, which are of course typical values for spacings between energy levels in the nucleus.

In terms of physical size, one could look at the uncertainty principle. The gamma ray momentum is $E/c$ and if we make a characteristic dimension $\Delta x$ be related to this by $$\Delta x\Delta p = \frac{E}{c} \sim \hbar,$$ $$ \Delta x \sim \frac{\lambda}{2\pi}.$$ Then the wavelength range corresponds to $10^{-15}< \Delta x < 10^{-12}$ m.

So the smallest wavelength you quote does indeed have some correspondence with the size scale of the nucleus through the typical energy scale and the uncertainty principle.