Find the number of photons emitted per second by a $25 \text{ W}$ source of monochromatic light of wavelength $6600 \text{ Å}$. What is the photoelectric current assuming $3 \%$ efficiency for the photoelectric effect?

The radiation corresponding to the $3 \rightarrow 2$ transition of a hydrogen atom falls on a gold surface to generate photoelectrons. These electrons are passed through a magnetic field of $5 \times 10^{-4} \, T$. Assume that the radius of the largest circular path followed by these electrons is $7 \, mm$. The work function of the metal is $..... \, eV$. (Mass of electron $= 9.1 \times 10^{-31} \, kg$)

The ratio of the wavelength of a photon of energy $E$ to that of an electron of the same energy is ($m=$ mass of an electron,$c=$ speed of light,$h=$ Planck's constant).

In a photocell,bichromatic light of wavelengths $2475 \ \mathring{A}$ and $6000 \ \mathring{A}$ is incident on a cathode whose work function is $4.8 \ eV$. If a uniform magnetic field of $3 \times 10^{-5} \ T$ exists parallel to the plate,the radius of the path described by the photoelectron will be ............ $cm$ (mass of electron $= 9 \times 10^{-31} \ kg$).

Given below are two statements:
Statement $I$: Out of microwaves,infrared rays,and ultraviolet rays,ultraviolet rays are the most effective for the emission of electrons from a metallic surface.
Statement $II$: Above the threshold frequency,the maximum kinetic energy of photoelectrons is inversely proportional to the frequency of the incident light.
In the light of the above statements,choose the correct answer from the options given below:

Energy of an electron and a photon are equal. If the wavelength of the electron is $1\,\mathring{A}$,then the wavelength of the photon is approximately ............. $\mathring{A}$.