Multiple Choice
The electron in a hydrogen atom absorbs a photon causing the electron to jump from the state n = 3 to the state n = 4. The frequency of the absorbed photon was __________ × 10¹⁴ Hz.
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9. Quantum Mechanics
Bohr Model
Multiple Choice
According to the Bohr model, which of the following statements is true about the energy levels of a hydrogen atom?
A
A hydrogen atom in the n = 2 state is at a lower energy than one in the n = 1 state.
B
The energy of a hydrogen atom is the same in all states.
C
A hydrogen atom in the n = 1 state is at a higher energy than one in the n = 3 state.
D
A hydrogen atom in the n = 3 state is at a higher energy than one in the n = 1 state.
Verified step by step guidance1
Understand the Bohr model: The Bohr model describes the hydrogen atom as having electrons in circular orbits around the nucleus, with each orbit corresponding to a specific energy level denoted by the principal quantum number n.
Recognize the energy level relationship: In the Bohr model, the energy of an electron in a hydrogen atom is quantized and depends on the principal quantum number n. The energy levels are given by the formula: E_n = -13.6 eV / n^2, where E_n is the energy of the level and n is the principal quantum number.
Analyze the energy level formula: Notice that as n increases, the magnitude of the energy (which is negative) decreases, meaning the energy becomes less negative and thus higher. Therefore, higher n values correspond to higher energy levels.
Evaluate the given statements: Compare the energy levels for different n values using the formula. For example, n = 1 has a lower energy (more negative) than n = 3, which means n = 3 is at a higher energy level than n = 1.
Identify the correct statement: Based on the analysis, the correct statement is that a hydrogen atom in the n = 3 state is at a higher energy than one in the n = 1 state, aligning with the energy level formula and the Bohr model's predictions.
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