Multiple Choice
Which of the following best describes an excited state of an atom?
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9. Quantum Mechanics
The Energy of Light
Multiple Choice
What is the energy (in joules) of an electron in a helium ion (He+) at the energy level n = 4? (Use the formula E = -Z^2 R_H / n^2, where Z is the atomic number, R_H = 2.18 × 10^{-18} J, and n is the principal quantum number.)
A
-1.36 × 10^{-19} J
B
-6.81 × 10^{-20} J
C
-2.18 × 10^{-18} J
D
-8.72 × 10^{-19} J
Verified step by step guidance1
Identify the given values from the problem: the atomic number \(Z\) for helium is 2, the Rydberg constant \(R_H\) is \(2.18 \times 10^{-18}\) J, and the principal quantum number \(n\) is 4.
Write down the formula for the energy of an electron in a hydrogen-like ion:
\(E = -\frac{Z^2 R_H}{n^2}\)
Substitute the known values into the formula: replace \(Z\) with 2, \(R_H\) with \(2.18 \times 10^{-18}\) J, and \(n\) with 4.
Calculate the numerator by squaring the atomic number: \(Z^2 = 2^2 = 4\), then multiply by \(R_H\) to get \(4 \times 2.18 \times 10^{-18}\) J.
Calculate the denominator by squaring the principal quantum number: \(n^2 = 4^2 = 16\), then divide the numerator by this value to find the energy \(E\).
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