The continuous part of $X$-ray spectrum is a result of the

A photon falls through a height of $1 \,km$ through the earth's gravitational field. To calculate the change in its frequency, take its mass to be $h v / c^{2}$. The fractional change in frequency $v$ is close to

A $100 \;W$ sodium lamp radiates energy uniformly in all directions. The lamp is located at the centre of a large sphere that absorbs all the sodium light which is incident on it. The wavelength of the sodium light is $589\; nm$.

$(a)$ What is the energy per photon associated with the sodium light?

$(b)$ At what rate are the photons delivered to the sphere?

The energy of a photon of wavelength $\lambda $ is given by

Both the nucleus and the atom of some element are in their respective first excited states. They get de-excited by emitting photons of wavelengths $\lambda _N,\,\lambda _A$  respectively. The ratio $\frac{{{\lambda _N}}}{{{\lambda _A}}}$  is closest to