Essential University Physics (3rd Edition)
Essential University Physics (3rd Edition)
3rd Edition
ISBN: 9780134202709
Author: Richard Wolfson
Publisher: PEARSON
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Chapter 36.1, Problem 36.1GI
To determine

The approximate estimate of the radial size of hydrogen atom in 2s state.

(a) a0

(b) 2a0

(c) 5a0

(d) 15a0

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Angular momentum and Spin. An electron in an H-atom has orbital angular momentum magnitude and z-component given by L² = 1(1+1)ħ², Lz = m₁h, 1 = 0,1,2,..., n 1 - m₁ = 0, ±1, ±2, ..., ±l 3 S² = s(s+1) h² = =h²₁ 4 Consider an excited electron (n > 1) on an H-atom. The total angular momentum ] = L + Š, whose magnitude and z-component follow a similar dependence to some quantum numbers j and m; as J² = j(j + 1)ħ², Jz = mjħ 1 S₂ = m₂h = ± = h Where j and m; are quantum numbers which assume values that jumps in steps of one such that j is non-negative and −j ≤ m¡ ≤ j. For a given quantum number 1, what are the (two) possible values for j? Clue: we can use the vector sum relation of angular momenta, then consider the z-component only.
= . Using the formula for the hydrogen atom energy levels, En constant can be written in terms of fundamental quantities, RH = Me 4 8€, ²h³c Me 4 1 860²h² n²¹ the Rydberg and its value approaches, RH → R∞ = 10,973,731.6 m-¹ in the limit u → me. (a) How would this constant be defined for a one-electron species containing Z protons in its nucleus? Consider how this changes the form of the Hamiltonian and the energy levels for that Hamiltonian. (b) The hydrogen atom emission lines in the Balmer series (n₂ = 2) lie in the visible portion of the electromagnetic spectrum. Would this also be true if Z> 1? Find the wavelength (in nm) of the n = 32 emission in hydrogen and that for a one-electron species with Z = 2. (You will be asked to report a quantity on the quiz that depends on these two values.)
e. The radial function for the 3s orbital in the hydrogen atom is given below: 3/2 (27 – 180 + 202)e (o = ) Zr ao = 52.92 pm R35 = ao. 27 [3ao- Calculate the distance(s) of the node(s) of the 3s orbital of the hydrogen atom from the nucleus.

Chapter 36 Solutions

Essential University Physics (3rd Edition)

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