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 $eV$)

$A$ 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 $e = 1.6 \times 10^{-19} \, C$.

Two parallel discs are connected by a rigid rod of length $L=0.5 \,m$ centrally. Each disc has a slit oppositely placed as shown in the figure. $A$ beam of neutral atoms is incident on one of the discs axially at different velocities $v$,while the system is rotated at an angular speed of $600 \,rev/s$,so that atoms only with a specific velocity emerge at the other end. Calculate the two largest speeds (in $m/s$) of the atoms that will emerge at the other end.

For a body moving with relativistic speed,if the velocity is doubled,then

The wave nature of light cannot explain the photoelectric effect because,in the photoelectric effect,it is observed that:

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