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![### Electron Transitions for the Hydrogen Atom
The diagram shows the electron transitions in a hydrogen atom for different series. Each colored line represents electron transitions from higher energy levels (n) to a specific lower energy level.
- **Lyman Series (Ultraviolet Region):**
- Transitions from n ≥ 2 to n = 1
- Represented by orange lines.
- **Balmer Series (Visible Region):**
- Transitions from n ≥ 3 to n = 2
- Represented by green lines.
- **Paschen Series (Infrared Region):**
- Transitions from n ≥ 4 to n = 3
- Represented by teal lines.
- **Brackett Series (Infrared Region):**
- Transitions from n ≥ 5 to n = 4
- Represented by blue lines.
### Problem Statement
The series limit wavelength of the Balmer series is emitted as the electron in the hydrogen atom falls from \( n = \infty \) to \( n = 2 \). What would be the specific wavelength of such a line?
### Hint
\[
\frac{1}{\lambda} = R_H\left(\frac{1}{n_{\text{final}}^2} - \frac{1}{n_{\text{initial}}^2}\right)
\]
where \( R_H \) (Rydberg constant) = \( 1.097 \times 10^7 \, \text{m}^{-1} \).
### Calculation
For series limit of the Balmer series:
- \( n_{\text{initial}} = \infty \)
- \( n_{\text{final}} = 2 \)
\[
\frac{1}{\lambda} = R_H\left(\frac{1}{2^2} - \frac{1}{\infty^2}\right) = R_H\left(\frac{1}{4} - 0 \right) = \frac{R_H}{4}
\]
\[
\lambda = \frac{4}{R_H} = \frac{4}{1.097 \times 10^7 \, \text{m}^{-1}}
\]
\[
\lambda \approx 364.6 \, \text{nm}
\]
### Multiple Choice Question
Select the correct specific wavelength for the Balmer series limit.](https://content.bartleby.com/qna-images/question/8c939cff-bc46-4066-b22a-d4e55e2c89ab/5633a1a5-f603-4542-b92f-985f33a09d6b/mk3l0om_processed.png)
Transcribed Image Text:### Electron Transitions for the Hydrogen Atom
The diagram shows the electron transitions in a hydrogen atom for different series. Each colored line represents electron transitions from higher energy levels (n) to a specific lower energy level.
- **Lyman Series (Ultraviolet Region):**
- Transitions from n ≥ 2 to n = 1
- Represented by orange lines.
- **Balmer Series (Visible Region):**
- Transitions from n ≥ 3 to n = 2
- Represented by green lines.
- **Paschen Series (Infrared Region):**
- Transitions from n ≥ 4 to n = 3
- Represented by teal lines.
- **Brackett Series (Infrared Region):**
- Transitions from n ≥ 5 to n = 4
- Represented by blue lines.
### Problem Statement
The series limit wavelength of the Balmer series is emitted as the electron in the hydrogen atom falls from \( n = \infty \) to \( n = 2 \). What would be the specific wavelength of such a line?
### Hint
\[
\frac{1}{\lambda} = R_H\left(\frac{1}{n_{\text{final}}^2} - \frac{1}{n_{\text{initial}}^2}\right)
\]
where \( R_H \) (Rydberg constant) = \( 1.097 \times 10^7 \, \text{m}^{-1} \).
### Calculation
For series limit of the Balmer series:
- \( n_{\text{initial}} = \infty \)
- \( n_{\text{final}} = 2 \)
\[
\frac{1}{\lambda} = R_H\left(\frac{1}{2^2} - \frac{1}{\infty^2}\right) = R_H\left(\frac{1}{4} - 0 \right) = \frac{R_H}{4}
\]
\[
\lambda = \frac{4}{R_H} = \frac{4}{1.097 \times 10^7 \, \text{m}^{-1}}
\]
\[
\lambda \approx 364.6 \, \text{nm}
\]
### Multiple Choice Question
Select the correct specific wavelength for the Balmer series limit.
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