$A$ sodium surface is illuminated by light of wavelength $3000\ \mathring A$. The work function of sodium is $2.6\ eV$. The maximum $K.E.$ of the emitted electrons is ........ $eV$.

The maximum kinetic energy of a photoelectron liberated from the surface of lithium with work function $2.35 \text{ eV}$ by electromagnetic radiation whose electric component varies with time as: $E=a[1+\cos(2 \pi f_1 t)] \cos(2 \pi f_2 t)$ (where $a$ is a constant) is (given $f_1=3.6 \times 10^{15} \text{ Hz}$,$f_2=1.2 \times 10^{15} \text{ Hz}$ and Planck's constant $h=6.6 \times 10^{-34} \text{ Js}$) (in $\text{ eV}$)

$A$ metal is exposed to light of wavelength $800 \, nm$ and emits photoelectrons with a certain kinetic energy. The maximum kinetic energy of the photoelectrons doubles when light of wavelength $500 \, nm$ is used. The work function of the metal is $... \, eV$ (Take $hc = 1230 \, eV \cdot nm$).

In the experiment of photoelectric effect, $K_{max}$ for a photoelectron is $K_0$. If the frequency of light is doubled, then $K_{max}$ is $3K_0$. What would be the value of $K_{max}$ if the frequency of light is tripled? (in terms of $K_0$)

Monochromatic radiation of wavelength $640.2 \;nm$ $(1 \;nm = 10^{-9} \;m)$ from a neon lamp irradiates a photosensitive material made of caesium on tungsten. The stopping voltage is measured to be $0.54 \;V$. The source is replaced by an iron source and its $427.2 \;nm$ line irradiates the same photo-cell. Predict the new stopping voltage (in $V$). (in $;V$)

The threshold wavelengths for photoelectric emission from two metals $A$ and $B$ are $400 \ nm$ and $800 \ nm$ respectively. The ratio of their work functions,$\phi_{A} : \phi_{B}$ is: