The de Broglie wavelength of a particle moving with a speed of $0.8 c$ is equal to the wavelength of a photon. If $c$ is the speed of light in vacuum, the ratio of the energy of the photon to the kinetic energy of the particle is:

The kinetic energy of emitted cathode rays is dependent on:

The ratio of the wavelength of a photon of energy $E$ to that of an electron of the same energy is ($m=$ mass of an electron,$c=$ speed of light,$h=$ Planck's constant).

$A$ light beam of wavelength $500 \, nm$ is incident on a metal having a work function of $1.25 \, eV$,placed in a magnetic field of intensity $B$. The electrons emitted perpendicular to the magnetic field $B$,with maximum kinetic energy,are bent into a circular arc of radius $30 \, cm$. The value of $B$ is $.... \times 10^{-7} \, T$.
Given $hc = 20 \times 10^{-26} \, J \cdot m$,mass of electron $m_e = 9 \times 10^{-31} \, kg$,and $e = 1.6 \times 10^{-19} \, C$.

Given below are two statements:
Statement $I$: Out of microwaves,infrared rays,and ultraviolet rays,ultraviolet rays are the most effective for the emission of electrons from a metallic surface.
Statement $II$: Above the threshold frequency,the maximum kinetic energy of photoelectrons is inversely proportional to the frequency of the incident light.
In the light of the above statements,choose the correct answer from the options given below:

Consider the following statements: $(1)$ Both wave and particle nature are required for a complete understanding of light. $(2)$ Light cannot exhibit both wave and particle nature simultaneously in a single experiment.