When the electromagnetic radiations of frequencies $4 \times 10^{15} \,Hz$ and $6 \times 10^{15} \,Hz$ fall on the same metal in different experiments,the ratio of maximum kinetic energy of electrons liberated is $1: 3$. The threshold frequency for the metal is ............... $\times 10^{15} Hz$.

$A$ light of wavelength $310 \,nm$ is used in a photoelectric experiment. The metal electrode of work function $2.5 \,eV$ is used in the experiment. The stopping potential for the photoelectrons will be (assume $hc = 1240 \,eV-nm$): (in $V$)

The photoelectric cut-off voltage in a certain experiment is $1.5 \; V$. What is the maximum kinetic energy of photoelectrons emitted?

In a photoelectric effect experiment,the cathode metal is exposed to light of wavelength $600 \ nm$. The maximum kinetic energy of the ejected electron doubles when light of wavelength $400 \ nm$ is used. The work function of the cathode metal is approximately: [Use $h=6.63 \times 10^{-34} \ J-s, c=3 \times 10^8 \ m/s$] (in $eV$)

When a certain metal surface is illuminated with light of frequency $v$,the stopping potential for the photoelectric current is $V_s$. When the same surface is illuminated by a light of frequency $v/2$,the stopping potential is $V_s/4$. The threshold frequency of photoelectric emission is

$A$ 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 ............. $V$.