QuestionJuly 7, 2025

A transition in the Bohr hydrogen atom from n=4 to n=2 occurs in the __ region of the electromagnetic spectrum. microwave visible infrared X-ray ultraviolet

A transition in the Bohr hydrogen atom from n=4 to n=2 occurs in the __ region of the electromagnetic spectrum. microwave visible infrared X-ray ultraviolet
A transition in the Bohr hydrogen atom from n=4 to n=2 occurs in the __ region of the electromagnetic spectrum. microwave visible infrared X-ray ultraviolet

Solution
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Answer

ultraviolet Explanation 1. Calculate the energy difference Use the formula for energy levels in a hydrogen atom: E_n = -\frac{13.6 \, \text{eV}}{n^2}. Calculate E_4 and E_2: - E_4 = -\frac{13.6}{4^2} = -0.85 \, \text{eV} - E_2 = -\frac{13.6}{2^2} = -3.4 \, \text{eV} 2. Determine the energy of the transition Calculate the energy difference: \Delta E = E_2 - E_4 = -3.4 - (-0.85) = -2.55 \, \text{eV}. 3. Identify the region of the electromagnetic spectrum The energy of 2.55 eV corresponds to the ultraviolet region.

Explanation

1. Calculate the energy difference<br /> Use the formula for energy levels in a hydrogen atom: $E_n = -\frac{13.6 \, \text{eV}}{n^2}$. Calculate $E_4$ and $E_2$:<br />- $E_4 = -\frac{13.6}{4^2} = -0.85 \, \text{eV}$<br />- $E_2 = -\frac{13.6}{2^2} = -3.4 \, \text{eV}$<br /><br />2. Determine the energy of the transition<br /> Calculate the energy difference: $\Delta E = E_2 - E_4 = -3.4 - (-0.85) = -2.55 \, \text{eV}$.<br /><br />3. Identify the region of the electromagnetic spectrum<br /> The energy of 2.55 eV corresponds to the ultraviolet region.
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