Physical Chemistry
2nd Edition
ISBN: 9781133958437
Author: Ball, David W. (david Warren), BAER, Tomas
Publisher: Wadsworth Cengage Learning,
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Chapter 11, Problem 11.63E
Interpretation Introduction
Interpretation:
The electrostatic potential energy
Concept introduction:
The work required to bring the charges together from an infinite distance to form the defined system is called electrostatic potential energy.
The electrostatic potential energy is calculated by using the formula,
The electrostatic potential energy depends on the distance between the nucleus and electron and not on the angles.
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Consider an electron in the N shell. (a) What is the smallest orbital angular momentum it could have? (b) What is the largest orbital angular momentum it could have? Express your answers in terms of h and in SI units. (c) What is the largest orbital angular momentum this electron could have in any chosen direction? Express your answers in terms of h and in SI units. (d) What is the largest spin angular momentum this electron could have in any chosen direction? Express your answers in terms of h and in SI units. (e) For the electron in part (c), what is the ratio of its spin angular momentum in the z-direction to its orbital angular momentum in the z-direction?
1. a) Calculate the numerical values of the energies of the first four energy levels in hydrogen in
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substituting n = 1, 2, 3, 4 into the equation you found in section (f) above. Show all work.
b) Use r = n²ħ²/(e²km) to calculate numerical values for the radii of the first four allowed
electron 'orbits' in hydrogen, in units of m. The radius of the 'orbit' closest to the nucleus is
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multiple of the Bohr radius, ie. when n = 1 then r = ao, if n = 2 then r = 2² ao, at n = 3 then r =
9 ao, etc.)
1
2
3
4
c) Summarize your numerical results in the following table;
Quantum number n Radius of electron's 'orbit' (m)
Electron Energy (J)
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Chapter 11 Solutions
Physical Chemistry
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