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
(a)
(b)
(c)
(d)
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Students have asked these similar questions
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)
Ch. 36.1 - Prob. 36.1GICh. 36.2 - Prob. 36.2GICh. 36.3 - Prob. 36.3GICh. 36.4 - Prob. 36.4GICh. 36.5 - Prob. 36.5GICh. 36 - Prob. 1FTDCh. 36 - Prob. 2FTDCh. 36 - Prob. 3FTDCh. 36 - Prob. 4FTDCh. 36 - Prob. 5FTD
Ch. 36 - Prob. 6FTDCh. 36 - Prob. 7FTDCh. 36 - Prob. 8FTDCh. 36 - Prob. 9FTDCh. 36 - Prob. 10FTDCh. 36 - Prob. 11FTDCh. 36 - Prob. 12FTDCh. 36 - What distinguishes a Bose-Einstein condensate from...Ch. 36 - Prob. 14ECh. 36 - Prob. 15ECh. 36 - Prob. 16ECh. 36 - Prob. 17ECh. 36 - Prob. 18ECh. 36 - Prob. 19ECh. 36 - Prob. 20ECh. 36 - Prob. 21ECh. 36 - Prob. 22ECh. 36 - Prob. 23ECh. 36 - Prob. 24ECh. 36 - Prob. 25ECh. 36 - Prob. 26ECh. 36 - Prob. 27ECh. 36 - Prob. 28ECh. 36 - Prob. 29ECh. 36 - Prob. 30ECh. 36 - Prob. 31ECh. 36 - Prob. 32ECh. 36 - Prob. 33ECh. 36 - Prob. 34PCh. 36 - Prob. 35PCh. 36 - Prob. 36PCh. 36 - Prob. 37PCh. 36 - Prob. 38PCh. 36 - Prob. 39PCh. 36 - Prob. 40PCh. 36 - Prob. 41PCh. 36 - Prob. 42PCh. 36 - Prob. 43PCh. 36 - Prob. 44PCh. 36 - Prob. 45PCh. 36 - Prob. 46PCh. 36 - Prob. 47PCh. 36 - Prob. 48PCh. 36 - Prob. 49PCh. 36 - Prob. 50PCh. 36 - Prob. 51PCh. 36 - Prob. 52PCh. 36 - Prob. 53PCh. 36 - Prob. 54PCh. 36 - Prob. 55PCh. 36 - Prob. 56PCh. 36 - Prob. 57PCh. 36 - Prob. 58PCh. 36 - Prob. 59PCh. 36 - Prob. 60PCh. 36 - Prob. 61PCh. 36 - Prob. 62PCh. 36 - Prob. 63PCh. 36 - Prob. 64PCh. 36 - Prob. 65PCh. 36 - Prob. 66PCh. 36 - Prob. 67PCh. 36 - Prob. 68PCh. 36 - Prob. 69PCh. 36 - Prob. 70PCh. 36 - Prob. 71PCh. 36 - Prob. 72PCh. 36 - Prob. 73PCh. 36 - Prob. 74PCh. 36 - Prob. 75PCh. 36 - Prob. 76PPCh. 36 - Prob. 77PPCh. 36 - Prob. 78PPCh. 36 - Prob. 79PP
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- A ground-state hydrogen atom is placed in a uniform magnetic field, and a photon is emitted in the transition from a spin-up to spin-down state. The wavelength of the photon is 168 µm. What is the strength of the magnetic field?arrow_forwardA beryllium ion with a single electron (denoted Be3+) is in an excited state with radius the same as that of the ground state of hydrogen. (a) What is n for the Be3+ ion? (b) How much energy in eV is needed to ionize the ion from this excited state?arrow_forwardIf an atom has an election in the n = 5 state with m = 3, what are the possible values of l?arrow_forward
- (a) How many electrons can be in the n=4 shell? (b) What are its subshells, and how many electrons can be in each?arrow_forwardExplain how a hydrogen atom in the ground state (l = 0) can interact magnetically with an external magnetic field.arrow_forwardCheck Your Understanding When an election in a hydrogen atom is in the first excited state, what prediction does the Bohr model give about its orbital speed and kinetic energy? What is the magnitude of its orbital angular momentum?arrow_forward
- What is the difference in energy between two states (n = 1; n = 2) of the Fe atom that originates this transition? What is the corresponding energy difference for the hydrogen atom? use this equation to calculate the energy difference ΔΕ 327²e}h’n²arrow_forwardAngular momentum and Spin. An electron in an H-atom has orbital angular momentum magnitude and z-component given by L² = 1(1+1)ħ², 1 = 0,1,2,..., n-1 Lz = m₂ħ, m₁ = 0, ±1, ±2,..., ±l 3 S² = s(s+1)h² = h², 4 Consider an excited electron (n > 1) on an H-atom. Sz = msh 1 =+=ħ Show that the minimum angle that the I can have with the z-axis is given by n-1 n L.min = cos Clue: the angle a vector with magnitude V from the z-axis can be computed from cos 0 = V²/Varrow_forwarda) In a sample of 300 hydrogen atoms in the n = 5 state, all the atoms return to the n = 2 state. i) Calculate the number of possible photon energies that will be emitted. Assume that all possible transitions occur. ii) Assuming that all possible downward transitions are equally probable, calculate the number of photons that will be emitted in each transition.arrow_forward
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