### Electron Transitions for the Hydrogen AtomThe 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: \( n= 5, 6, 7, \ldots \)### QuestionThe 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.

Initial orbit of electron is Final orbit of electron is Rydberg constant is Note:Find:Wavelength of…

Wavelength of the Balmer series is emitted as the electron in the hydrogen atom falls from, according to the above figure) n = (3 to ∞) to n = 2. What would be the specific wavelength of such a line for n; = 4? [Hint :1/λ = RH(1/n/² - 1/n²), R₁ being Rydberg constant = 1.097 × 107 /m]

Wavelength of the Balmer series is emitted as the electron in the hydrogen atom falls from, according to the above figure) n = (3 to ∞) to n = 2. What would be the specific wavelength of such a line for n; = 4? [Hint :1/λ = RH(1/n/² - 1/n²), R₁ being Rydberg constant = 1.097 × 107 /m]

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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.

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