NCERT Solutions for Chapter: Dual Nature of Radiation and Matter, Exercise 2: VSA

A proton and an $\alpha$-particle are accelerated, using the same potential difference. How are the de-Broglie wavelengths ${\lambda }_p$and ${\lambda }_{\alpha }$ related to each other?

In the explanation of photoelectric effect, we assume one photon of frequency $v$ collides with an electron and transfers its energy. This leads to the equation for the maximum energy $E_{max}$ of the emitted electron as

$E_{max}=hv={\varphi }_0$ where ${\varphi }_0$ is the work function of the metal. If an electron absorbs $2$ photons (each of frequency $v$), what will be the maximum energy for the emitted electron?

In the explanation of photo electric effect, we assume one photon of frequency $v$ collides with an electron and transfers its energy. This leads to the equation for the maximum energy $E_{max}$ of the emitted electron as

$E_{max}=hv={\varphi }_0$ where ${\varphi }_0$ is the work function of the metal. If an electron absorbs $2$ photons (each of frequency $v$), what will be the maximum energy for the emitted electron? Why is this fact (two photon absorption) not taken into consideration in our discussion of the stopping potential?

There are materials which absorb photons of shorter wavelength and emit photons of longer wavelength. Can there be stable substances which absorb photons of larger wavelength and emit light of shorter wavelength.

Do all the electrons that absorb a photon come out as photoelectrons?

There are two sources of light, each emitting with a power of $100 \mathrm{W}$. One emits X-rays of wavelength $1 \mathrm{nm}$ and the other visible light at $500 \mathrm{nm}$. Find the ratio of number of photons of X-rays to the photons of visible light of the given wavelength?