College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Related questions
Question
![### Electron Transitions for the Hydrogen Atom
The diagram illustrates the electron transitions for the hydrogen atom, highlighting several prominent series of transitions:
1. **Lyman Series (Ultraviolet Region)**
- Transitions: \( E(n) \to E(n=1) \)
- Energy levels: \( n = 2, 3, 4, \ldots \)
2. **Balmer Series (Visible Region)**
- Transitions: \( E(n) \to E(n=2) \)
- Energy levels: \( n = 3, 4, 5, \ldots \)
3. **Paschen Series (Infrared Region)**
- Transitions: \( E(n) \to E(n=3) \)
- Energy levels: \( n= 4, 5, 6, \ldots \)
4. **Brackett Series (Infrared Region)**
- Transitions: \( E(n) \to E(n=4) \)
- Energy levels: \( n= 5, 6, 7, \ldots \)
### Question
The wavelength of the Balmer series is emitted as the electron in the hydrogen atom falls from \( n \) (where \( n \) ranges from 3 to \(\infty\)) to \( n = 2 \). What would be the specific wavelength of such a line for \( n_i = 4 \)?
**Hint:**
\[ \frac{1}{\lambda} = R_H \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right) \]
where \(R_H\) is the Rydberg constant \( = 1.097 \times 10^7 \, \text{m}^{-1}\).
### Options:
1. \( 1122 \, \text{nm} \)
2. \( 486 \, \text{nm} \)
3. \( 562 \, \text{nm} \)
4. \( 780 \, \text{nm} \)
To solve this problem, substitute the values \( n_f = 2 \) and \( n_i = 4 \) into the formula provided. This calculation will yield the wavelength of the emitted photon during the electron transition.](https://content.bartleby.com/qna-images/question/0fcb0af8-b750-4635-b3ee-2f0c31e9ebdb/93c6dfbe-2047-4f7c-9b10-b12a40ce3297/5gmavdk_processed.png)
Transcribed Image Text:### Electron Transitions for the Hydrogen Atom
The diagram illustrates the electron transitions for the hydrogen atom, highlighting several prominent series of transitions:
1. **Lyman Series (Ultraviolet Region)**
- Transitions: \( E(n) \to E(n=1) \)
- Energy levels: \( n = 2, 3, 4, \ldots \)
2. **Balmer Series (Visible Region)**
- Transitions: \( E(n) \to E(n=2) \)
- Energy levels: \( n = 3, 4, 5, \ldots \)
3. **Paschen Series (Infrared Region)**
- Transitions: \( E(n) \to E(n=3) \)
- Energy levels: \( n= 4, 5, 6, \ldots \)
4. **Brackett Series (Infrared Region)**
- Transitions: \( E(n) \to E(n=4) \)
- Energy levels: \( n= 5, 6, 7, \ldots \)
### Question
The wavelength of the Balmer series is emitted as the electron in the hydrogen atom falls from \( n \) (where \( n \) ranges from 3 to \(\infty\)) to \( n = 2 \). What would be the specific wavelength of such a line for \( n_i = 4 \)?
**Hint:**
\[ \frac{1}{\lambda} = R_H \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right) \]
where \(R_H\) is the Rydberg constant \( = 1.097 \times 10^7 \, \text{m}^{-1}\).
### Options:
1. \( 1122 \, \text{nm} \)
2. \( 486 \, \text{nm} \)
3. \( 562 \, \text{nm} \)
4. \( 780 \, \text{nm} \)
To solve this problem, substitute the values \( n_f = 2 \) and \( n_i = 4 \) into the formula provided. This calculation will yield the wavelength of the emitted photon during the electron transition.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by stepSolved in 3 steps with 16 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- The orbital radii of a hydrogen-like atom is given by the equation What is the radius of the first Bohr orbit in (a) He+,(b) Li2+, and (c) Be3+arrow_forwardWhat frequency of light, in THz (Terahertz, or 10^12 Hz), is needed for an electron in a hydrogen atom to go from the n = 2 state to the n = 3 state?arrow_forwardThe total probability of finding an electron in the hydrogen atom is related to the integral ∫ r2 e-2r/ao dr Where r is the distance of the electron from the nucleus and ao is the Bohr radius. Evaluate thisintegral.arrow_forward
- The radial probability density of a hydrogen wavefunction in the 1s state is given by P(r) = |4rr2 (R13 (r))²| and the radial wavefunction R1s (r) = a0 , where ao is 3/2 the Bohr radius. Using the standard integral x"e - ka dx n! calculate the standard deviation in the radial position from the nucleus for the 1s state in the Hydrogen atom. Give your answer in units of the Bohr radius ao.arrow_forwardPlease answer (i), (v), and (vi). Thank you! (i) Using Bohr model for atomic hydrogen, obtain energy levels for the 2s, 3s and 3p states in the actual number with the unit of [eV]. We consider a transition that electron in the 3p state emits a photon and make a transition to the 2s state. What is the frequency v of this photon ? (ii) Now we do not include electron spin angular momentum, and just estimate an effect of a magnetic field B on this transition (Normal Zeeman effect) with orbital angular momentum. How many lines of optical transition do we expect ? What is the interval of the frequency in the field B = 0.1 Tesla ? (iii) In this situation, we do not expect transition from 3s to 2s state if the electron is initially in the 3s state, Explain the reason. (iv) We now consider an effect of magnetic field B to a free electron spin (not in Hydrogen, but a free electron). The magnetic field of B = 1.0 Tesla will split the energy level into two (Zeeman) levels. Obtain the level…arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
University Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSON
Introduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press 
Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Lecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON