Chapter 33: Q1P (page 1001)

A certain helium–neon laser emits red light in a narrow band of wavelengths centered at $632.8 nm$ and with a “wavelength width” (such as on the scale of Fig. 33-1) of $0.0100 nm$ . What is the corresponding “frequency width” for the emission?

Short Answer

Expert verified

The frequency width of the emission is $7.49 \times 10^{9} Hz$

Step by step solution

Step 1: Listing the given quantities

Wavelength, $λ = 623.8 nm = 623.8 \times 10^{- 9} m$ .

Wavelength width, $Δ λ = 0.0100 nm = 0.0100 \times 10^{- 9} m$ .

Speed of light, $c = 3 \times 10^{8} m/s$ .

Step 2: Understanding the concepts of frequency and wavelength

In wavelength scale Fig. 33-1, each scale marker represents a change in wavelength and corresponding frequency. A certain scale denotes the electromagnetic spectrum. In this problem, we will calculate the frequency width of the He-Ne laser required for the emission using the formula for the change in frequency in terms of velocity of light and wavelength.

Formula:

$Δ f = |Δ (\frac{c}{λ})|$

Step 3: Calculations of the frequency width of the emission

Since $Δ λ ≪ λ,$ we will find $Δ f$ as,

$\begin{array}{rcl} Δ f & = & |Δ (\frac{c}{λ})| \\ = & \frac{c Δ λ}{λ^{2}} \end{array}$

Substitute the values in the above expression, and we get,

$\begin{array}{rcl} Δ f & = & \frac{(3 \times 10^{8}) (623.8 \times 10^{- 9})}{{(0.0100 \times 10^{- 9})}^{2}} \\ = & 7.49 \times 10^{9} Hz \end{array}$

The frequency width of the emission is $7.49 \times 10^{9} Hz$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

A certain helium–neon laser emits red light in a narrow band of wavelengths centered at $632.8 nm$ and with a “wavelength width” (such as on the scale of Fig. 33-1) of $0.0100 nm$ . What is the corresponding “frequency width” for the emission?

Short Answer

Step by step solution

Step 1: Listing the given quantities

Step 2: Understanding the concepts of frequency and wavelength

Step 3: Calculations of the frequency width of the emission

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Radiation

Thermodynamics

Electric Charge Field and Potential

Famous Physicists

Physical Quantities And Units

Engineering Physics

Study anywhere. Anytime. Across all devices.

A certain helium–neon laser emits red light in a narrow band of wavelengths centered at632.8nm and with a “wavelength width” (such as on the scale of Fig. 33-1) of0.0100nm. What is the corresponding “frequency width” for the emission?

Short Answer

Step by step solution

Step 1: Listing the given quantities

Step 2: Understanding the concepts of frequency and wavelength

Step 3: Calculations of the frequency width of the emission

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Radiation

Thermodynamics

Electric Charge Field and Potential

Famous Physicists

Physical Quantities And Units

Engineering Physics

Study anywhere. Anytime. Across all devices.

A certain helium–neon laser emits red light in a narrow band of wavelengths centered at $632.8 nm$ and with a “wavelength width” (such as on the scale of Fig. 33-1) of $0.0100 nm$ . What is the corresponding “frequency width” for the emission?