Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 23: Problem 33

Calculate the energy of the photon emitted when a hydrogen atom undergoes a spin-flip transition. How many such photons would it take to equal the energy of a single \(\mathrm{H}_{\alpha}\) photon of wavelength \(656.3 \mathrm{~nm}\) ?

Short Answer

Expert verified
The energy of the photon emitted during a spin-flip transition in a hydrogen atom is calculated and then the energy of a single \(\mathrm{H}_{\alpha}\) photon is computed. The number of spin-flip photons needed to equal the energy of one \(\mathrm{H}_{\alpha}\) photon is the result of the division of the energy of the \(\mathrm{H}_{\alpha}\) photon by the energy of the spin-flip photon.

Step by step solution

01

Determining The Energy of Photon Emitted During Spin-Flip Transition

The frequency of the photon emitted during a spin-flip transition (also known as hyperfine transition) in a hydrogen atom is approximately \(1420.405751776 \mathrm{~MHz}\). Using the equation \(E=hf\), where \(h = 6.62607015 × 10^{-34} \mathrm{~m}^2 \mathrm{~kg} / \mathrm{~s}\) is Planck's Constant, we can calculate the energy \(E\). Converting the frequency from MHz to Hz (\(1 \mathrm{~MHz} = 1×10^6 \mathrm{~Hz}\)), we get \(f = 1420.405751776 × 10^6 \mathrm{~Hz}\). Therefore, \(E = h × f = 6.62607015 × 10^{-34} \mathrm{~m}^2 \mathrm{~kg} /\mathrm{~s} × 1420.405751776 × 10^6 \mathrm{~Hz}\).
02

Calculating The Energy of a Single \(\mathrm{H}_{\alpha}\) Photon

The \(\mathrm{H}_{\alpha}\) line corresponds to a wavelength of \(656.3 \mathrm{~nm}\). First change the wavelength to meters (\(1 \mathrm{~nm} = 1 × 10^{-9} \mathrm{~m}\)), giving \(λ = 656.3 × 10^{-9} \mathrm{~m}\). To find the frequency, we use the equation \(c= λf\), where \(c = 2.998 × 10^8 \mathrm{~m/s}\) is the speed of light. Thus, \(f = c/λ\). Then, use this frequency in the equation \(E = hf\) to calculate the energy of the \(\mathrm{H}_{\alpha}\) photon.
03

Determining The Number of Photons Needed

In order to find out how many photons from spin-flip transitions would be needed to equal the energy of one \(\mathrm{H}_{\alpha}\) photon, we simply divide the energy of the \(\mathrm{H}_{\alpha}\) photon by the energy of the spin-flip photon, which calculated in Step 1.

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!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

What is the evidence that there is a supermassive black hole at the center of our Galaxy? How is it possible to determine the mass of this black hole?

From what you know about stellar evolution, the interstellar medium, and the density-wave theory, explain the appearance and structure of the spiral arms of grand-design spiral galaxies.

Student book bags often contain a wide collection of oddshaped objects. Each person in your group should rummage through their own book bags and find one object that is most similar to the Milky Way Galaxy in shape. List the items from each group member's belongings and describe what about the items is similar to the shape of our Galaxy and what about the items is not similar, then indicate which of the items is the closest match.

Explain why globular clusters spend most of their time in the galactic halo, even though their eccentric orbits take them close to the galactic center.

What is the winding dilemma? What does it tell us about the nature of spiral arms?
See all solutions

Recommended explanations on Physics Textbooks

Physics of Motion

Read Explanation

Space Physics

Read Explanation

Measurements

Read Explanation

Nuclear Physics

Read Explanation

Circular Motion and Gravitation

Read Explanation

Electricity

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free