Hydrogen Electron Energy Calculation
The energy of an electron in a hydrogen atom is determined by its principal quantum number, n. The energy levels follow the formula:
\(E_n = \frac{E_1}{n^2}\)
where E1 is the ground state energy (−13.6 eV) and n is the orbit number.
Alternatively, the energy of an electron in orbit n can be related to its energy in orbit m using the ratio:
\(E_n = E_m \times \frac{m^2}{n^2}\)
Step-by-Step Calculation
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Identify the given values:
- Energy in the second orbit (\(n=2\)): \(E_2 = -3.4\) eV.
- We need to find the energy in the fourth orbit (\(n=4\)).
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Apply the energy ratio formula:
\(E_4 = E_2 \times \frac{2^2}{4^2}\)
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Substitute the known values:
\(E_4 = -3.4 \text{ eV} \times \frac{4}{16}\)
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Simplify the expression:
\(E_4 = -3.4 \text{ eV} \times \frac{1}{4}\)
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Calculate the final energy:
\(E_4 = -0.85 \text{ eV}\)
The energy of the electron in the fourth orbit is −0.85 eV.
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