Published by:
CGP EDU Academic Team
Published on: September 12, 2026
Energy of an electron in
orbit of hydrogen atom is
Text Solution
Verified by ExpertsThe correct answer is:
B
To find the energy of an electron in the nth orbit of a hydrogen atom, we use the formula:
$$E_n = -\frac{k e^2}{2 a_0 n^2}$$
where:
- $k$ is Coulomb's constant.
- $e$ is the charge of the electron.
- $a_0$ is the Bohr radius.
- n is the principal quantum number.
The energy levels are quantized and become less negative (closer to zero) as n increases, indicating that energy increases as the electron moves to higher orbits. Examining the options provided, we can see that Option B appropriately captures this energy in the format of the expected values for the electron in hydrogen atom, which is also consistent with known energy calculations for hydrogenic systems.
Therefore, the correct option is B.
$$E_n = -\frac{k e^2}{2 a_0 n^2}$$
where:
- $k$ is Coulomb's constant.
- $e$ is the charge of the electron.
- $a_0$ is the Bohr radius.
- n is the principal quantum number.
The energy levels are quantized and become less negative (closer to zero) as n increases, indicating that energy increases as the electron moves to higher orbits. Examining the options provided, we can see that Option B appropriately captures this energy in the format of the expected values for the electron in hydrogen atom, which is also consistent with known energy calculations for hydrogenic systems.
Therefore, the correct option is B.
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