What is the frequency of light emitted when the electron in a hydrogen atom undergoes a transition from level n = 6 to level n = 4? (c=3.00×10⁸ m/s,h=6.63×10^-34 J·s,R_H=2.179×10^-18 J) A)2.63×10^-6 Hz B)3.8×10⁵ Hz C)3.97×10²⁷ Hz D)7.57×10^-20 Hz E)1×10¹⁴ Hz

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Quizplus · Accepted Answer

The frequency of light emitted can be calculated using the formula: $ f = \frac{\Delta E}{h} $, where $\Delta E = R_H \left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right) $. For the transition from n=6 to n=4, $\Delta E = 2.179 \times 10^{-18} \left(\frac{1}{4^2} - \frac{1}{6^2}\right) $. Solving this gives $\Delta E \approx 2.179 \times 10^{-18} \times 0.0463 \approx 1.01 \times 10^{-19} $ J. Then, $ f = \frac{1.01 \times 10^{-19}}{6.63 \times 10^{-34}} \approx 1.52 \times 10^{14} $ Hz, which is closest to option E.

What Is the Frequency of Light Emitted When the Electron