Maharashtra Board Solutions for Chapter: Dual Nature of Radiation and Matter, Exercise 9: Exercises

What will be the energy of each photon in monochromatic light of frequency $5\times {10}^{14} \mathrm{Hz}$?

Observations from an experiment on photoelectric effect for the stopping potential by varying the incident frequency were plotted. The slope of the linear curve was found to be approximately $4.1\times {10}^{-15} \mathrm{V} \mathrm{s}$. Given that the charge of an electron is $1.6\times {10}^{-19} \mathrm{C}$, find the value of the Planck's constant $\mathrm{h}$.

Photocurrent recorded in the micro ammeter in an experimental set-up of photoelectric effect vanishes when the retarding potential is more than $0.8 \mathrm{V}$ if the wavelength of incident radiation is $4950 \stackrel{\mathrm{o}}{\mathrm{A}}$. If the sources of incident radiation is changed, the stopping potential turns out to be $1.2 \mathrm{V}$. Find the work function of the cathode material and the wavelength of the second source. Take $h=6.6\times {10}^{-34} \mathrm{J} \mathrm{s}$ and $c=3\times {10}^8 \mathrm{m}/\mathrm{s}$.

Radiation of wavelength $4500 \stackrel{\mathrm{o}}{\mathrm{A}}$ is incident on a metal having work function $2.0 \mathrm{eV}$. Due to the presence of a magnetic field B, the most energetic photoelectrons emitted in a direction perpendicular to the field move along a circular path of radius $20 \mathrm{cm}$. What is the value of the magnetic field B? Take the mass of electron$=9.1\times {10}^{-31} \mathrm{kg}$, the charge of electron $=1.6\times {10}^{-19} \mathrm{C}$, Planck's constant $=6.6\times {10}^{-34} \mathrm{J} \mathrm{s}$.

Given the following data for incident wavelength and the stopping potential obtained from an experiment on photoelectric effect, estimate the value of Planck's constant and the work function of the cathode material. What is the threshold frequency and corresponding wavelength? What is the most likely metal used for emitter?

Two particles have the same de Broglie wavelength and one is moving four times as fast as the other. If the slower particle is an $\mathrm{\alpha }$-particle, what are the possibilities for the other particle?

What is the speed of a proton having de Broglie wavelength of $0.08 \stackrel{\mathrm{o}}{\mathrm{A}}$?

In nuclear reactors, neutrons travel with energies of $5\times {10}^{-21} \mathrm{J}$. Find their speed and wavelength.