$A$ photon and an electron have equal energy $E$. The ratio $\lambda_{\text{photon}} / \lambda_{\text{electron}}$ is proportional to:

In a photoelectric experiment,light of wavelength $800 \ nm$ produces photoelectrons with the smallest de Broglie wavelength of $1 \ nm$. Then the work function of the metal used in the experiment is nearly (in $eV$)

The radiation corresponding to the $3 \rightarrow 2$ transition of a hydrogen atom falls on a gold surface to generate photoelectrons. These electrons are passed through a magnetic field of $5 \times 10^{-4} \, T$. Assume that the radius of the largest circular path followed by these electrons is $7 \, mm$. The work function of the metal is $..... \, eV$. (Mass of electron $= 9.1 \times 10^{-31} \, kg$)

In the photoelectric effect:
$A.$ The photocurrent is proportional to the intensity of the incident radiation.
$B.$ The maximum kinetic energy with which photoelectrons are emitted depends on the intensity of incident light.
$C.$ The maximum kinetic energy with which photoelectrons are emitted depends on the frequency of incident light.
$D.$ The emission of photoelectrons requires a minimum threshold intensity of incident radiation.
$E.$ The maximum kinetic energy of the photoelectrons is independent of the frequency of the incident light.
Choose the correct answer from the options given below:

One day on a spacecraft corresponds to $2$ days on the earth. The speed of the spacecraft relative to the earth is

The de-Broglie wavelength of an electron is the same as that of a photon. If the velocity of the electron is $25 \%$ of the velocity of light,then the ratio of the $K.E.$ of the electron to the $K.E.$ of the photon will be: