The particle nature and wave nature of electromagnetic waves and electrons can be demonstrated by which of the following?

$A$ radiation of $3.8 eV$ falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field of $2 \times 10^{-4} T$. If the radius of the largest circular path followed by these electrons is $30 mm$,then the work function of the metal is (Mass of electron $m_{e} = 9 \times 10^{-31} kg$) (in $eV$)

When a light source of power $P$ emitting monochromatic light of wavelength $\lambda$ is kept at a distance $r$ from a photosensitive surface of work function $\phi$ and surface area $A$,which of the following is the wrong option?

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

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?

Consider the following statements $A$ and $B$ and identify the correct choice in the given answers.
$A$. Tightly bound electrons of target material scatter $X$-ray photon,resulting in the Compton effect.
$B$. Photoelectric effect takes place with free electrons.