(a) Explanation Write the Schrodinger’s equation. − ℏ 2 2 m e ( d 2 ψ d r 2 + 2 r d ψ d r ) − V ψ = E ψ Here, ψ is the wavefunction, V is the potential, E is the energy and m e is the mass of electron. Write the expression for potential. V = − k e e 2 r Here, e is the unit of charge and k e is the coulomb constant. Substitute the given wave function and V in Schrodinger’s equation to check the validity. − ℏ 2 2 m e [ d 2 d r 2 ( 1 π a 0 3 e − r / a 0 ) + 2 r ( − 1 π a 0 5 e − r / a 0 ) ] − k e e 2 r ψ (b) To determine Energy of 1 s state.

Physics for Scientists and Engineers with Modern Physics

10th Edition

ISBN: 9781337553292

Author: Raymond A. Serway, John W. Jewett

Publisher: Cengage Learning

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Question

Chapter 41, Problem 16P

(a)

To determine

Whether wave function of 1s state satisfies shcrodinger’s equation.

(b)

To determine

Energy of 1s state.

Expert Solution & Answer

Chapter 41 Solutions

Physics for Scientists and Engineers with Modern Physics

Ch. 41.3 - Prob. 41.1QQ Ch. 41.3 - Prob. 41.2QQ Ch. 41.4 - Prob. 41.3QQ Ch. 41.4 - Prob. 41.4QQ Ch. 41.8 - Prob. 41.5QQ Ch. 41 - Prob. 1P Ch. 41 - Prob. 2P Ch. 41 - Prob. 3P Ch. 41 - Prob. 4P Ch. 41 - Prob. 5P

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For an electron in a hydrogen atom in the n=2 state, compute: (a) the angular momentum; (b) the kinetic energy; (c) the potential energy; and (d) the total energy.

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