Photons of energy $7 \,eV$ are incident on two metals $A$ and $B$ with work functions $6 \,eV$ and $3 \,eV$,respectively. The minimum de-Broglie wavelengths of the emitted photoelectrons with maximum kinetic energies are $\lambda_A$ and $\lambda_B$ respectively,where $\lambda_A / \lambda_B$ is nearly

For a metal with a work function of $6.6 \text{eV}$, which of the following wavelengths of incident radiation does not cause the photoelectric effect (in $\text{nm}$)? (Take Planck's constant $h = 6.6 \times 10^{-34} \text{J s}$ and speed of light $c = 3 \times 10^8 \text{m/s}$)

Ultraviolet light of wavelength $300 \ nm$ and intensity $1.0 \ W/m^2$ falls on the surface of a photosensitive material. If $1\%$ of the incident photons produce photoelectrons,then the number of photoelectrons emitted from an area of $1.0 \ cm^2$ of the surface is nearly

$A$ photosensitive surface made of cesium on tungsten is irradiated by monochromatic radiation of wavelength $640.2 \ nm$ $(1 \ nm = 10^{-9} \ m)$ from a neon bulb. The measured stopping potential is $0.54 \ V$. If the source is replaced by another source and the same photocell is irradiated by a line of $427.2 \ nm$,what will be the new stopping potential in $V$?

$A$ metal surface is illuminated by radiation of wavelength $4500 \; \mathring A$. The ejected photoelectron enters a constant magnetic field of $2 \; mT$ making an angle of $90^{\circ}$ with the magnetic field. If it starts revolving in a circular path of radius $2 \; mm$,the work function of the metal is approximately ............. $eV$.

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 . . . . . . .