Embibe Experts Solutions for Chapter: Dual Nature of Matter and Radiation, Exercise 2: Level 2

The de-Broglie wavelength of an electron is the same as that of a $50 \mathrm{keV}$ $\mathrm{X}$-ray photon. The ratio of the energy of the photon to the kinetic energy of the electron is (the energy equivalent of electron mass is $0.5 \mathrm{MeV}$)

The de-Broglie wavelength of an electron moving with a velocity $\frac{c}{2}$ ($c=$velocity of light in vacuum) is equal to the wavelength of a photon. The ratio of the kinetic energies of electron and photon is

The de-Broglie wavelength of an electron in the ground state of the hydrogen atom is

The threshold frequency for a certain metal is $3.3\times {10}^{14} \mathrm{Hz}$. If light of frequency $8.2\times {10}^{14} \mathrm{Hz}$ is incident on the metal, then the cut-off voltage for the photoelectric emission is approximately is $n \mathrm{volt}$. The value of $n$ is

The work functions of silver and sodium are $4.6$ and $2.3 \mathrm{eV}$, respectively. The ratio of the slope of the stopping potential versus frequency plot for silver to that of sodium is

The anode voltage of a photocell is kept fixed. The wavelength $\lambda$ of the light falling on the cathode is gradually changed. The plate current $I$ of photocell varies as follows:

In a photoelectric experiment, with light of wavelength $\lambda ,$ the fastest electron has speed $v.$ If the exciting wavelength is changed to $\frac{3\lambda }{4},$ the speed of the fastest emitted electron will become

In the photoelectric experiment, if we use a monochromatic light, the $I-V$ curve is as shown. If work function of the metal is $2\mathrm{eV},$ estimate the power of light used. (Assume efficiency of photo emission is ${10}^{-3}\%,$ i.e. number of photoelectrons emitted are ${10}^{-3}\%$ of number of photons incident on metal.)