When light of frequencies ${\nu _1}$ and ${\nu _2}$ $({\nu _1} > {\nu _2})$ is incident on a metal surface,the ratio of the maximum kinetic energy of the emitted photoelectrons is $1:k$. What is the threshold frequency of the metal?

In a photoelectric experiment,three different lights are incident on a metal with a work function of $1.5 \ eV$. Light $A$ has a wavelength of $200 \ nm$ and an intensity of $1.8 \ W/m^2$,light $B$ has a wavelength of $400 \ nm$ and an intensity of $1 \ W/m^2$,and light $C$ has a wavelength of $600 \ nm$ and an intensity of $0.5 \ W/m^2$. The photocurrent versus voltage is measured. Which graphs correspond to which light?

$A$ cobalt $(Co)$ plate is placed at a distance of $1 \,m$ from a point source of power $1 \,W$. Assume a circular area of the plate of radius $r = 1 \,Å$ is exposed to the radiation and ejects photoelectrons. The light energy is considered to be spread uniformly and the work function of cobalt is $5 \,eV$. The minimum time the target should be exposed to the light source to eject a photoelectron (assuming no reflection losses) is: (in $\,s$)

The threshold frequency of a photosensitive material is equal to the frequency of the $H_{\alpha}$ line of hydrogen. If a photon whose frequency is equal to the frequency of the $H_{\beta}$ line of hydrogen is incident on this photosensitive material,the maximum kinetic energy of the emitted photoelectrons is ($R$ = Rydberg's constant,$h$ = Planck's constant,and $c$ = speed of light in vacuum).

Photons with energy $5\, eV$ are incident on a cathode $C$ of a photoelectric cell. The maximum kinetic energy of the emitted photoelectrons is $2\, eV$. When photons of energy $6\, eV$ are incident on $C$,no photoelectrons will reach the anode $A$ if the stopping potential of $A$ relative to $C$ is .............. $V$.

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 . . . . . . .