The image contains the mathematical expression for the hydrogen 1s wavefunction. It is represented as follows:\[ \psi_{1s} = \frac{1}{\sqrt{\pi}} \left( \frac{1}{a_0} \right)^{3/2} e^{-r/a_0} \]**Explanation:**- **ψ_{1s}**: This represents the wavefunction for the 1s orbital of a hydrogen atom.- **π**: Represents the mathematical constant pi, approximately equal to 3.14159.- **a_0**: Known as the Bohr radius, it is a physical constant approximately equal to 0.529 Ångströms.- **r**: The radial distance from the nucleus.- **e^{-r/a_0}**: An exponential decay factor that describes how the wavefunction decreases with increasing distance from the nucleus.This formula is fundamental in quantum mechanics for understanding electron distribution in a hydrogen atom. **Calculate:**a. The most likely radius of an electron in the 1s orbital of a hydrogen atom.b. The radius that encompasses an 80% probability of finding the electron in a 1s orbital of a hydrogen atom.

Answered: Image /qna-images/answer/cbb91650-b087-4cc0-8a23-521f59175d81.jpg

Answered: Calculate: a. The most likely radius of…

Calculate: a. The most likely radius of an electron in the 1s orbital of a hydrogen atom b. The radius that encompasses an 80% probability of finding the electron in a 1s orbital of a hydrogen atom.

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

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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Question

The image contains the mathematical expression for the hydrogen 1s wavefunction. It is represented as follows:

\[ \psi_{1s} = \frac{1}{\sqrt{\pi}} \left( \frac{1}{a_0} \right)^{3/2} e^{-r/a_0} \]

**Explanation:**

- **ψ_{1s}**: This represents the wavefunction for the 1s orbital of a hydrogen atom.

- **π**: Represents the mathematical constant pi, approximately equal to 3.14159.

- **a_0**: Known as the Bohr radius, it is a physical constant approximately equal to 0.529 Ångströms.

- **r**: The radial distance from the nucleus.

- **e^{-r/a_0}**: An exponential decay factor that describes how the wavefunction decreases with increasing distance from the nucleus.

This formula is fundamental in quantum mechanics for understanding electron distribution in a hydrogen atom.

**Calculate:**

a. The most likely radius of an electron in the 1s orbital of a hydrogen atom.

b. The radius that encompasses an 80% probability of finding the electron in a 1s orbital of a hydrogen atom.

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