$A$ zinc ball of radius $1 \,cm$ is charged to a potential of $-0.5 \,V$. The ball is illuminated by a monochromatic ultraviolet light with a wavelength of $290 \,nm$. The photoelectric threshold for zinc is $332 \,nm$. The potential of the ball after a prolonged exposure to the ultraviolet light is ............. $V$.

Light of two different frequencies with photon energies of $1 \ eV$ and $2.5 \ eV$ are incident one after another on a metal surface having a work function of $0.5 \ eV$. The ratio of the maximum kinetic energy of the emitted photoelectrons will be:

When light of intensity $1 \ W/m^2$ and wavelength $5 \times 10^{-7} \ m$ is incident on a surface, it is completely absorbed. If $100$ photons emit one electron and the surface area is $1 \ cm^2$, what is the photoelectric current?

Two identical photo-cathodes receive light of frequencies $f_1$ and $f_2$. If the velocities of the photoelectrons (of mass $m$) coming out are respectively $v_1$ and $v_2$,then:

For a certain metal,when monochromatic light of wavelength $\lambda$ is incident,the stopping potential for photoelectrons is $3V_0$. When the same metal is illuminated by light of wavelength $2\lambda$,then the stopping potential becomes $V_0$. The threshold wavelength for photoelectric emission for the given metal is $\alpha\lambda$. The value of $\alpha$ is . . . . . . .

Consider a metal exposed to light of wavelength $600 \, nm$. The maximum kinetic energy of the emitted electron doubles when light of wavelength $400 \, nm$ is used. Find the work function of the metal in $eV$. (in $, eV$)