Multiple Choice
Which particles did Niels Bohr use in his experiments that led to the development of the Bohr model of the atom?
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9. Quantum Mechanics
Bohr Model
Multiple Choice
What is the energy change (ΔE, in joules) for the transition of an electron from n = 6 to n = 3 in a hydrogen atom according to the Bohr model?
A
-4.68 \(\times\) 10^{-19} \(\text{ J}\)
B
+4.68 \(\times\) 10^{-19} \(\text{ J}\)
C
-2.18 \(\times\) 10^{-18} \(\text{ J}\)
D
-1.94 \(\times\) 10^{-19} \(\text{ J}\)
Verified step by step guidance1
Recall that the energy levels of a hydrogen atom in the Bohr model are given by the formula:
\(E_n = -2.18 \times 10^{-18} \times \frac{1}{n^2}\) joules, where \(n\) is the principal quantum number.
Calculate the energy of the electron at the initial level \(n=6\) using the formula:
\(E_6 = -2.18 \times 10^{-18} \times \frac{1}{6^2}\).
Calculate the energy of the electron at the final level \(n=3\) using the formula:
\(E_3 = -2.18 \times 10^{-18} \times \frac{1}{3^2}\).
Find the energy change \(\Delta E\) for the transition by subtracting the initial energy from the final energy:
\(\Delta E = E_3 - E_6\).
Interpret the sign of \(\Delta E\): a negative value means the electron releases energy (emission), and a positive value means it absorbs energy (absorption).
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