An electron in a harmonic oscillator potential well and the value of the corresponding spring constant is 12.5 N/m.What is the frequency of light emitted when the electron jumps from one level to the next? A)7.16 * 10¹⁴ Hz B)5.90 * 10¹⁴ Hz C)6.32 * 10¹⁴ Hz D)6.88 * 10¹⁴ Hz

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Quizplus · Accepted Answer

The frequency of light emitted when an electron jumps from one level to the next in a harmonic oscillator potential well can be calculated using the formula for the frequency of a quantum harmonic oscillator, $f = \frac{1}{2\pi}\sqrt{\frac{k}{m}}$, where $k$ is the spring constant and $m$ is the mass of the electron. Given $k = 12.5 \, \text{N/m}$ and the mass of an electron $m = 9.109 \times 10^{-31} \, \text{kg}$, the calculation yields a frequency close to the value given in option B, when considering the energy difference between levels is quantized as $\Delta E = hf$, with $h$ being Planck's constant.

An Electron in a Harmonic Oscillator Potential Well and the Value