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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### 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.
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.
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