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

An electromagnetic wave of wavelength $\lambda$ is incident on a photosensitive surface of negligible work function. If the photoelectrons emitted from this surface have the de-Broglie wavelength $\lambda_{1}$,then:

$A$ monochromatic light is incident on a metallic plate having work function $\phi$. An electron,emitted normally to the plate from a point $A$ with maximum kinetic energy,enters a constant magnetic field,perpendicular to the initial velocity of electron. The electron passes through a curve and hits back the plate at a point $B$. The distance between $A$ and $B$ is (Given: The magnitude of charge of an electron is $e$ and mass is $m$,$h$ is Planck's constant,and $c$ is velocity of light. Take the magnetic field exists throughout the path of electron).

Assertion $(A)$: In the photoelectric effect,on increasing the intensity of light,both the number of electrons emitted and the kinetic energy of each of them increase,but the photoelectric current remains unchanged.
Reason $(R)$: The photoelectric current depends only on the wavelength of light.

An electron is moving through a field. It is moving $(i)$ opposite to an electric field and $(ii)$ perpendicular to a magnetic field as shown. For each situation,determine the de-Broglie wavelength of the electron.

Statement $(I)$ : By increasing the potential difference between cathode and anode continuously in a photoelectric experiment,the photocurrent always increases continuously.
Statement $(II)$ : If two photons $A$ and $B$ of energies $2.5 \ eV$ and $3.5 \ eV$ respectively fall on a metal surface of work function $2.0 \ eV$,then the ratio of maximum kinetic energies emitted between $A$ and $B$ is $3$.
Statement $(III)$ : The maximum energy needed by an electron to come out from metal surface is called the work function of the metal.
Which of the following is correct?