(a) Explanation Write the equation for the energy levels of hydrogen. E n = − 1 ( 4 π ε 0 ) 2 m r e 4 2 n 2 ℏ 2 Here, E n is the energy of the level with principal quantum number n m r is the reduced mass e is the magnitude of the charge of electron ℏ is h 2 π where h is the Planck’s constant ε 0 is a constant Substitute 1 for n in the above equation to find the total energy of the 1 s state. E 1 = − 1 ( 4 π ε 0 ) 2 m r e 4 2 ( 1 ) 2 ℏ 2 = − 1 ( 4 π ε 0 ) 2 m r e 4 2 ℏ 2 (1) Write the equation for the potential energy of hydrogen atom. U ( r ) = − 1 4 π ε 0 e 2 r (2) Here, r is the distance from the center of the nucleus Equate equations (1) and (2) (b) To determine The probability of the electron being found in the classically forbidden region.

University Physics with Modern Physics, Volume 2 (Chs. 21-37); Mastering Physics with Pearson eText -- ValuePack Access Card (14th Edition)

14th Edition

ISBN: 9780134265414

Author: Hugh D. Young, Roger A. Freedman

Publisher: PEARSON

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Question

Chapter 41, Problem 41.49P

(a)

To determine

The value of r at which the potential energy U(r) of the hydrogen atom in the 1s state becomes equal to the total energy E .

(b)

To determine

The probability of the electron being found in the classically forbidden region.

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Chapter 41, Problem 41.48P

Chapter 41, Problem 41.50P

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Chapter 41 Solutions

University Physics with Modern Physics, Volume 2 (Chs. 21-37); Mastering Physics with Pearson eText -- ValuePack Access Card (14th Edition)

Ch. 41.1 - Prob. 41.1TYU Ch. 41.2 - Prob. 41.2TYU Ch. 41.3 - Prob. 41.3TYU Ch. 41.4 - In this section we assumed that the magnetic field...Ch. 41.5 - In which of the following situations is the...Ch. 41.6 - Prob. 41.6TYU Ch. 41.7 - Prob. 41.7TYU Ch. 41.8 - Prob. 41.8TYU Ch. 41 - Prob. 41.1DQ Ch. 41 - Prob. 41.2DQ

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The value of r at which the potential energy U ( r ) of the hydrogen atom in the 1 s state becomes equal to the total energy E .

Solution Summary: The author explains the value of r at which the potential energy of the hydrogen atom in the 1s state becomes equal to the total energy E.

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The value of r at which the potential energy U(r) of the hydrogen atom in the 1s state becomes equal to the total energy E .

The probability of the electron being found in the classically forbidden region.

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Chapter 41 Solutions