In an experiment on the photoelectric effect,the slope of the cut-off voltage versus frequency of incident light is found to be $4.12 \times 10^{-15} \; V \cdot s$. Calculate the value of Planck's constant.

Light of wavelength $\lambda_{\text{ph}}$ falls on a cathode plate inside a vacuum tube as shown in the figure. The work function of the cathode surface is $\phi$ and the anode is a wire mesh of conducting material kept at a distance $d$ from the cathode. $A$ potential difference $V$ is maintained between the electrodes. If the minimum de Broglie wavelength of the electrons passing through the anode is $\lambda_e$,which of the following statement$(s)$ is(are) true?

Light of wavelength $488 \, nm$ produced by an Argon laser is used in the photoelectric effect. When light from this spectral line is incident on the cathode, the stopping potential of the photoelectrons is $0.38 \, V$. The work function of the cathode material is (in $ \, eV$)

When photons of energy $1 \ eV$ and $2.5 \ eV$ are incident on a metal surface with a work function of $0.5 \ eV$,what is the ratio of the maximum kinetic energies of the emitted photoelectrons?

Energy of the incident photons on the metal surface is initially $4W$ and then $6W$,where $W$ is the work function of that metal. The ratio of the maximum velocities of the emitted photoelectrons is:

The work function of a metal is $2.51 \ eV$. What is its threshold frequency?