Bohr atom: What is the frequency of the light emitted by atomic hydrogen with m = 8 and n = 12? (The Rydberg constant is R = 1.097 × 10⁷ m^-1;^c= 3.00 × 10⁸ m/s.) A) 2.86 × 10¹³ Hz B) 1.43 × 10¹³ Hz C) 7.46 × 10¹³ Hz D) 8.82 × 10¹³ Hz E) 1.05 × 10¹³ Hz

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Quizplus · Accepted Answer

The frequency of the light emitted can be calculated using the formula derived from the Bohr model and the Rydberg formula for hydrogen: $$f = R \cdot c \cdot \left( \frac{1}{m^2} - \frac{1}{n^2} \right)$$ where $R$ is the Rydberg constant ($1.097 \times 10^{7} \, \text{m}^{-1}$), $c$ is the speed of light ($3.00 \times 10^{8} \, \text{m/s}$), $m$ is the lower energy level (8), and $n$ is the higher energy level (12). Plugging in the values: $$f = 1.097 \times 10^{7} \times 3.00 \times 10^{8} \times \left( \frac{1}{8^2} - \frac{1}{12^2} \right)$$ $$f = 2.86 \times 10^{13} \, \text{Hz}$$

Bohr Atom: What Is the Frequency of the Light Emitted