Dual Nature of Radiation and Matter — Practice

Question 1

The work function of a metal is 2.0 eV. Find the maximum kinetic energy of photoelectrons when light of energy 3.2 eV falls on it.

Accepted Answer

Subtract the work function from the photon energy, working entirely in electronvolts. Answer: 1.2 eV.

Question 2

Find the energy in electronvolts of a photon of wavelength 620 nm.

Accepted Answer

Use E = hc/lambda, or the shortcut that E in eV is about 1240 divided by the wavelength in nm. Answer: 2.0 eV.

Question 3

Find the de Broglie wavelength of an electron moving at 2.0 x 10^6 m/s.

Accepted Answer

Apply lambda = h/mv with the electron mass 9.1 x 10^-31 kg. Answer: 3.6 x 10^-10 m.

Question 4

The threshold wavelength of a metal is 500 nm. Find its work function and the stopping potential when light of 400 nm falls on it.

Accepted Answer

Convert the threshold wavelength to a work function, then apply Einstein's equation. Answer: Work function 2.48 eV; stopping potential 0.62 V.

Question 5

Light of frequency 1.5 times the threshold frequency falls on a metal of work function 3.0 eV. Find the maximum kinetic energy of the photoelectrons.

Accepted Answer

Express the incident photon energy as a multiple of the work function, since the threshold frequency corresponds to it exactly. Answer: 1.5 eV.

Question 6

A 60 W lamp emits monochromatic light of wavelength 600 nm. Find how many photons it emits per second.

Accepted Answer

Find the energy per photon first, then divide the power by it. Answer: About 1.8 x 10^20 photons per second.

Question 7

An electron and a proton have the same kinetic energy. Which has the longer de Broglie wavelength, and by what factor?

Accepted Answer

Write lambda in terms of kinetic energy and mass, then take the ratio. Answer: The electron, by the square root of the mass ratio, about 43 times.

Question 8

When light of wavelength 350 nm falls on a metal the stopping potential is 1.2 V. Find the threshold wavelength of the metal.

Accepted Answer

Find the photon energy and subtract the stopping energy to get the work function, then convert back to a wavelength. Answer: About 545 nm.

Question 9

Find the minimum wavelength of X-rays produced by electrons accelerated through 50 kV, and explain why a sharp cut-off exists.

Accepted Answer

Set the whole kinetic energy equal to a single photon's energy, which is the most that can be radiated at once. Answer: 2.5 x 10^-11 m; the cut-off exists because no photon can exceed the electron's total energy.

Practice — Dual Nature of Radiation and Matter

Sign in to save attempts to your dashboard and track your accuracy over time

Find a verified tutor

Join a live course

Browse coaching centres

About

Categories

Support

Documentation

Get Study Tips & Updates

Download Our App

Download for iOS

Download for Android

Popular Cities