Embibe Experts Solutions for Chapter: Dual Nature of Matter and Radiation, Exercise 1: JEE Main - 25 Feb 2021 Shift 2

As shown in the figure, in Young's double slit experiment, a thin plate of thickness $t=10 \mathrm{\mu m}$ and refractive index $\mu =1.2$ is inserted infront of slit $S_1$. The experiment is conducted in air ($\mu =1$) and uses a monochromatic light of wavelength $\lambda =500 \mathrm{nm}$. Due to the insertion of the plate, central maxima is shifted by a distance of $x{\beta }_0$. ${\beta }_0$ is the fringe-width before the insertion of the plate. The value of the $x$ is ______.

The ratio of de-Broglie wavelength of an $\alpha$-particle and a proton accelerated from rest by the same potential is $\frac{1}{\sqrt{m}}$ , the value of $m$ is:

A small object at rest, absorbs a light pulse of power $20 \mathrm{mW}$ and duration $300 \mathrm{ns}$. Assuming speed of light as $3 \times {10}^8 \mathrm{m} {\mathrm{s}}^{-1}$. The momentum of the object becomes equal to :

An electron accelerated through a potential difference $V_1$ has a de-Broglie wavelength of $\lambda$. When the potential is changed to $V_2$, its de-Broglie wavelength increases by $50\%$. The value of $\left(\frac{V_1}{V_2}\right)$ is equal to :

If a source of electromagnetic radiation having power $15 \mathrm{kW}$ produces ${10}^{16}$ photons per second, the radiation belongs to a part of spectrum is :

(Take Planck constant $h = 6\times {10}^{-34} \mathrm{J} \mathrm{s})$

If the two metals $A$ and $B$ are exposed to radiation of wavelength $350 \mathrm{nm}$. The work functions of metals $A$ and $B$ are $4.8 \mathrm{eV} \text{and} 2.2 \mathrm{eV}$. Then choose the correct option

A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of $\lambda$. An alpha particle having certain kinetic energy has the same de-Brogle wavelength $\lambda$. The ratio of kinetic energy of proton and that of alpha particle is :

The threshold frequency of metal is $f_0$. When the light of frequency $2f_0$ is incident on the metal plate, the maximum velocity of photoelectron is $v_1$. When the frequency of incident radiation is increased to $5f_0$. the maximum velocity of photoelectrons emitted is $v_2$. The ratio of $v_1$ to $v_2$ is: