The electron in the hydrogen atom jumps from excited state $(n = 3)$ to its ground state $(n = 1)$ and the photons thus emitted irradiate a photosensitive material. If the work function of the material is $5.1 \, eV$,the stopping potential is estimated to be (the energy of the electron in $n^{th}$ state $E_n = \frac{-13.6}{n^2} \, eV$) (in $, V$)

An electromagnetic wave of wavelength $\lambda$ is incident on a photosensitive surface of negligible work function. If the photoelectron emitted from the surface has mass $m$ and de-Broglie wavelength $\lambda_{d}$,then

The threshold wavelength for the photoelectric effect on sodium is $5000\;\mathring{A}$. Its work function is:

In a photoelectric experiment,a graph is drawn with stopping potential along $Y$-axis and the frequency of the incident light along $X$-axis. If the graph is a straight line which makes an angle $\theta$ with $Y$-axis,then $\tan \theta=$ ($h$-Planck's constant,$e$-charge of electron).

An electron and a proton are separated by a large distance. The electron starts approaching the proton with an initial kinetic energy of $3 \, eV$. The proton captures the electron and forms a hydrogen atom in the second excited state. The resulting photon is incident on a photosensitive metal with a threshold wavelength of $4000 \, Å$. What is the maximum kinetic energy of the emitted photoelectron? (In $eV$)

$A$ silver ball of radius $4.8 \ cm$ is suspended by a thread in a vacuum chamber. $UV$ light of wavelength $200 \ nm$ is incident on the ball for some time,during which a total energy of $1 \times 10^{-7} \ J$ falls on the surface. Assuming that on average one out of $10^3$ incident photons is able to eject an electron,the potential on the sphere will be ............ $V$.