If the threshold wavelength for a metal is $\lambda_0$ and the wavelength of incident light is $\lambda$,what will be the maximum velocity of the emitted electrons?

How many emission spectral lines are possible when a hydrogen atom is excited to the $n$th energy level?

The energy of an electron in a Hydrogen atom is given by the expression:

If the work function for the photoelectron emission of a metal is $3.75 \ eV$,then the threshold wavelength of the radiation needed for the ejection of the electron is approximately (in $nm$)

$A$ source of monochromatic radiation of wavelength $400 \, nm$ provides $1000 \, J$ of energy in $10 \, seconds$. When this radiation falls on the surface of sodium,$x \times 10^{20}$ electrons are ejected per second. Assume that wavelength $400 \, nm$ is sufficient for ejection of electrons from the surface of sodium metal. The value of $x$ is $......$. (Nearest integer) $(h = 6.626 \times 10^{-34} \, Js)$

$A$ metal surface is illuminated by light of two different wavelengths $248 \ nm$ and $310 \ nm$. The maximum speeds of the photoelectrons corresponding to these wavelengths are $u_1$ and $u_2$ respectively. If the ratio $u_1 : u_2 = 2 : 1$ and $hc = 1240 \ eV \ nm$,the work function of the metal is nearly $:-$ (in $eV$)