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 = 5. The frequency of the absorbed photon was __________ × 10^14 Hz.
9. Quantum Mechanics
Bohr Model
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According to the Bohr Model, to which energy level would an electron in a hydrogen atom be excited if it absorbed a photon with an energy of 1230 kJ/mol, starting from the ground state?
A
Energy level 4
B
Energy level 2
C
Energy level 7
D
Energy level 1
Verified step by step guidance1
First, understand that the Bohr Model describes electrons in hydrogen atoms as occupying specific energy levels, denoted by the principal quantum number \( n \). The ground state corresponds to \( n = 1 \).
Next, recognize that the energy of a photon absorbed by an electron can be used to calculate the change in energy levels. The energy of the photon is given as 1230 kJ/mol.
Convert the energy from kJ/mol to J per electron. Since 1 mol contains Avogadro's number of electrons (approximately \( 6.022 \times 10^{23} \)), divide the energy by this number to find the energy per electron.
Use the formula for the energy difference between levels in the Bohr Model: \( \Delta E = -2.18 \times 10^{-18} \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right) \) J, where \( n_i \) is the initial energy level and \( n_f \) is the final energy level. Set \( n_i = 1 \) for the ground state.
Solve for \( n_f \) by rearranging the formula to find the energy level that corresponds to the calculated energy per electron. This will determine the final energy level to which the electron is excited.
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