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}

Answer: (A)

Verified step by step guidance

1. 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.
2. Calculate the energy of the electron at the initial level \(n=6\) using the formula: \(E_6 = -2.18 \times 10^{-18} \times \frac{1}{6^2}\).
3. Calculate the energy of the electron at the final level \(n=3\) using the formula: \(E_3 = -2.18 \times 10^{-18} \times \frac{1}{3^2}\).
4. Find the energy change \(\Delta E\) for the transition by subtracting the initial energy from the final energy: \(\Delta E = E_3 - E_6\).
5. Interpret the sign of \(\Delta E\): a negative value means the electron releases energy (emission), and a positive value means it absorbs energy (absorption).