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Multiple Choice
Which of the electron transitions represents an example of absorption with the greatest energy?
A
n = 1 to n = 4
B
n = 2 to n =3
C
n = 6 to n = 7
D
n = 5 to n = 6
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1
Understand that electron transitions involve an electron moving between energy levels in an atom. Absorption occurs when an electron moves to a higher energy level, requiring energy input.
Recall that the energy difference between levels is given by the formula: \( E = -R_H \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \), where \( R_H \) is the Rydberg constant, \( n_1 \) is the initial energy level, and \( n_2 \) is the final energy level.
Recognize that the greater the difference between \( n_1 \) and \( n_2 \), the greater the energy absorbed. Therefore, transitions from lower to higher levels with larger gaps will absorb more energy.
Compare the given transitions: \( n = 1 \) to \( n = 4 \), \( n = 2 \) to \( n = 3 \), \( n = 6 \) to \( n = 7 \), and \( n = 5 \) to \( n = 6 \). Calculate the energy difference for each using the formula.
Identify that the transition \( n = 1 \) to \( n = 4 \) involves the largest change in energy levels, thus representing absorption with the greatest energy.