rydberg formula

Question

Using Rydberg formula, what is the wavelength of light emitted when an electron in hydrogen atom transitions from n = 3 to n = 2? (R = 1.097 × 10⁷ m⁻¹)

RankGuru · Accepted Answer

1. **Rydberg Equation**: $\frac{1}{\lambda} = R \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} ight)$.
2. **Identify Orbits**: $n_1 = 2$ (lower) and $n_2 = 3$ (higher).
3. **Set up Calculation**:
   - $\frac{1}{\lambda} = 1.097 	imes 10^7 \left( \frac{1}{4} - \frac{1}{9} ight)$
   - $\frac{1}{\lambda} = 1.097 	imes 10^7 \left( \frac{9-4}{36} ight) = 1.097 	imes 10^7 	imes \frac{5}{36}$.
4. **Invert to find $\lambda$**:
   - $\lambda = \frac{36}{5 	imes 1.097 	imes 10^7} \approx 6.56 	imes 10^{-7}$ m.
5. **Convert Units**: $6.56 	imes 10^{-7}$ m $= 656 	ext{ nm}$.

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