Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

Answers without the blur.

Just sign up for free and you're in.

Short Answer

An ultraviolet lamp emits light of wavelength 400 nm at the rate of 400 W. An infrared lamp emits light of wavelength 700 nm, also at the rate of 400 W. (a) Which lamp emits photons at the greater rate and (b) what is that greater rate?

(a) The infrared lamp emits photons at greater rate.

(b) The rate of emitted protons is $1.4 \times 10^{21} p h o t o n s / s$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Describe the expression of emission rate and energy of the photon

The expression of emission rate is given by,

$R = \frac{P}{E_{p}}$

Here, P is power

The energy of photon of wavelength $λ$ is given by,

role="math" localid="1663136623680" $E_{p} = \frac{h c}{λ}$

Here, h is the Planck’s constant, and c is the speed of light.

Step 2: Determine the lamp that emit photons at the greater rate

(a)

The wavelength of the photon and energy of the photon has indirect relationship so; the wavelength of the photon will be larger, when the energy is smaller. Here, the wavelength of the infrared light is more than the ultraviolet light.

Therefore, the energy of the infrared photon is less than the ultraviolet photon. But the power emitted by both lamps is same.

$Number of photons emitted per second = \frac{Energy emitted per second}{Energy of each photon}$

Here, the energy emitted per second is constant and equal to 400 W .

$Number of photons emitted per second \propto \frac{1}{Energy of each photon}$

From the above relation, it can be observed that if the energy of the infrared photon is less than the ultraviolet photon then the number of photon emitted by the infrared light will be more.

Therefore, the infrared lamp emits photons at greater rate.

Step 3: Determine the rate of emission of the photon

(b)

The expression to calculate the emission rate is given by,

$R = \frac{P λ}{h c}$ .... (1)

Substitute 400 W for P, 700 nm for $λ$ , $6.626 \times 10^{- 34} J \cdot s$ for h, and $3 \times 10^{8} m s^{- 1}$ for c in equation (1).

$R = \frac{(400 W) (700 n m)}{(6.626 \times 10^{- 34} J . s) (3 \times 10^{8} m / s)} R = \frac{(400 W) (700 n m) \frac{1 m}{10^{9} n m}}{(6.626 \times 10^{- 34} J . s) (3 \times 10^{8} m / s)} R = 1.4 \times 10^{21} p h o t o n / s$

Therefore, the rate of emitted protons is $1.4 \times 10^{21} p h o t o n / s$ .

Find Study Materials for

Create Study Materials

Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

An ultraviolet lamp emits light of wavelength 400 nm at the rate of 400 W. An infrared lamp emits light of wavelength 700 nm, also at the rate of 400 W. (a) Which lamp emits photons at the greater rate and (b) what is that greater rate?

Step by Step Solution

Step 1: Describe the expression of emission rate and energy of the photon

Step 2: Determine the lamp that emit photons at the greater rate

Step 3: Determine the rate of emission of the photon

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

An ultraviolet lamp emits light of wavelength 400 nm at the rate of 400 W. An infrared lamp emits light of wavelength 700 nm, also at the rate of 400 W. (a) Which lamp emits photons at the greater rate and (b) what is that greater rate?

Step by Step Solution

Step 1: Describe the expression of emission rate and energy of the photon

Step 2: Determine the lamp that emit photons at the greater rate

Step 3: Determine the rate of emission of the photon

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Work Energy and Power

Radiation

Astrophysics

Physics of Motion

Scientific Method Physics

Fluids

Torque and Rotational Motion

Nuclear Physics

Fields in Physics

Measurements

Space Physics

Electricity

Physical Quantities and Units

Medical Physics

Electrostatics

Further Mechanics and Thermal Physics

Mechanics and Materials

Engineering Physics

Energy Physics

Force

Particle Model of Matter

Waves Physics

Magnetism

Modern Physics

Atoms and Radioactivity

Dynamics

Electricity and Magnetism

Conservation of Energy and Momentum

Fundamentals of Physics

Kinematics Physics

Circular Motion and Gravitation

Linear Momentum

Rotational Dynamics

Oscillations

Translational Dynamics

Geometrical and Physical Optics

Thermodynamics

Magnetism and Electromagnetic Induction

Electromagnetism

Electric Charge Field and Potential

Turning Points in Physics