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Calculate the energy of an electron in n=2 state of a hydrogen atom. Give your answer in attojoules (aJ).

Calculate the energy of an electron in n=2 state of a hydrogen atom. Give your answer in attojoules (aJ).

Chemistry
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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Calculate the energy of an electron in n=2 state of a hydrogen atom. Give your answer in attojoules (aJ).
The image contains the following formula for calculating the energy levels of an electron in a hydrogen atom: \[ E_n = -2.17987 \times 10^{-18} \, \text{J} \left( \frac{1}{n^2} \right) \] **Explanation:** - **\( E_n \):** Represents the energy of an electron at a particular energy level \( n \). - **\( -2.17987 \times 10^{-18} \, \text{J} \):** This is a constant in joules, known as the Rydberg energy for a hydrogen atom. - **\( n \):** The principal quantum number, which denotes the energy level of the electron. It can take positive integer values (n = 1, 2, 3,...). - **\( \left( \frac{1}{n^2} \right) \):** This fraction determines how the energy levels change with different values of \( n \). The formula calculates how the energy decreases as the principal quantum number \( n \) increases, corresponding to higher energy levels further from the nucleus.
Transcribed Image Text:The image contains the following formula for calculating the energy levels of an electron in a hydrogen atom: \[ E_n = -2.17987 \times 10^{-18} \, \text{J} \left( \frac{1}{n^2} \right) \] **Explanation:** - **\( E_n \):** Represents the energy of an electron at a particular energy level \( n \). - **\( -2.17987 \times 10^{-18} \, \text{J} \):** This is a constant in joules, known as the Rydberg energy for a hydrogen atom. - **\( n \):** The principal quantum number, which denotes the energy level of the electron. It can take positive integer values (n = 1, 2, 3,...). - **\( \left( \frac{1}{n^2} \right) \):** This fraction determines how the energy levels change with different values of \( n \). The formula calculates how the energy decreases as the principal quantum number \( n \) increases, corresponding to higher energy levels further from the nucleus.
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