Multiple Choice
What is the energy (in J) of a photon required to excite an electron from n = 2 to n = 6 in a He⁺ ion? Submit an answer to three significant figures.
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9. Quantum Mechanics
Bohr Equation
Multiple Choice
Determine the end (final) value of n in a hydrogen atom transition, if the electron starts in n = 5 and the atom releases a photon of light with an energy of 4.5738 × 10-19 J.
A
4
B
2
C
3
D
1
Verified step by step guidance1
Understand that the problem involves an electron transition in a hydrogen atom, where the electron moves from a higher energy level (n = 5) to a lower energy level, releasing a photon in the process.
Recall the formula for the energy of a photon released during an electron transition in a hydrogen atom: E = -R_H * (1/n_final^2 - 1/n_initial^2), where R_H is the Rydberg constant (approximately 2.18 × 10^-18 J).
Substitute the given values into the formula: E = 4.5738 × 10^-19 J, n_initial = 5, and solve for n_final.
Rearrange the formula to solve for n_final: 1/n_final^2 = 1/n_initial^2 - E/R_H.
Calculate the possible values of n_final by testing integer values (n = 1, 2, 3, 4) to find which one satisfies the equation, ensuring the calculated energy matches the given photon energy.
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