What is the energy, in J, of light that must be absorbed by a hydrogen atom to transition an electron from n = 3 to n = 6?

Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
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**Question:**

What is the energy, in joules (J), of light that must be absorbed by a hydrogen atom to transition an electron from \( n = 3 \) to \( n = 6 \)?

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**Explanation:**

This question focuses on calculating the energy required for an electron in a hydrogen atom to move between energy levels using the Bohr model. According to the Bohr model, the energy of an electron in a particular orbit is quantized and can be given by the equation:

\[ E_n = -\frac{13.6 \, \text{eV}}{n^2} \]

To find the energy of the light absorbed, one must calculate the energy difference between the initial and final states:

1. Calculate \( E_3 \) for \( n = 3 \).
2. Calculate \( E_6 \) for \( n = 6 \).
3. Find the difference \( \Delta E = E_6 - E_3 \).
4. Convert the energy from electron volts (eV) to joules (J).

This energy difference is the amount of energy the photon must have for the electron to make the upward transition from \( n = 3 \) to \( n = 6 \).
Transcribed Image Text:**Question:** What is the energy, in joules (J), of light that must be absorbed by a hydrogen atom to transition an electron from \( n = 3 \) to \( n = 6 \)? --- **Explanation:** This question focuses on calculating the energy required for an electron in a hydrogen atom to move between energy levels using the Bohr model. According to the Bohr model, the energy of an electron in a particular orbit is quantized and can be given by the equation: \[ E_n = -\frac{13.6 \, \text{eV}}{n^2} \] To find the energy of the light absorbed, one must calculate the energy difference between the initial and final states: 1. Calculate \( E_3 \) for \( n = 3 \). 2. Calculate \( E_6 \) for \( n = 6 \). 3. Find the difference \( \Delta E = E_6 - E_3 \). 4. Convert the energy from electron volts (eV) to joules (J). This energy difference is the amount of energy the photon must have for the electron to make the upward transition from \( n = 3 \) to \( n = 6 \).
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