Multiple Choice
For hydrogen, what is the wavelength of the photon emitted when an electron drops from the n=3 level to the n=2 level? The Rydberg constant is 1.097 × 10^7 m^-1.
9. Quantum Mechanics
Bohr Equation
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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.
A
1.96 x 10^-18 J
B
5.45 x 10^-19 J
C
4.09 x 10^-18 J
D
2.18 x 10^-18 J
Verified step by step guidance1
Understand that the problem involves calculating the energy required to excite an electron in a hydrogen-like ion, He⁺, from one energy level to another. This requires using the formula for the energy difference between two levels in a hydrogen-like atom.
Recall the formula for the energy levels of a hydrogen-like ion: , where is the atomic number, is the Rydberg constant (2.18 x 10^-18 J), and is the principal quantum number.
Calculate the energy for the initial state (n = 2) using the formula: .
Calculate the energy for the final state (n = 6) using the formula: .
Determine the energy of the photon required for the transition by calculating the difference between the energy levels: . This will give you the energy in joules needed to excite the electron from n = 2 to n = 6.
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