A silver sphere of radius $1\ cm$ and work function $4.7 \ eV$ is suspended from an insulating thread in free-space. It is under continuous illumination of $200 \ nm$ wavelength light. As photoelectrons are emitted, the sphere gets charged and acquires a potential. The maximum number of photoelectrons emitted from the sphere is $A \times 10^2$ (where $1 < A < 10$ ). The value of  $'Z '$ is

The energy of a photon of wavelength $\lambda $ is given by

An astronaut floating freely in space decides to use his flash light as a rocket. He shines a $10$ watt light beam in a fixed direction so that he acquires momentum in the opposite direction. If his mass is $80$ kg, how long must he need to reach a velocity of $1$ $ms^{-1}$

The momentum of a photon of energy $h\nu $ will be

Energy of a quanta of frequency ${10^{15}}Hz$ and $h = 6.6 \times {10^{ - 34}}J{\rm{ - }}\sec $ will be

The momentum of a photon in an $X-$ ray beam of ${10^{ - 10}}$ metre wavelength is