FUND OF PHYSICS VOL 1-W/WILEYPLUS >IC<
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ISBN: 9781119012658
Author: Halliday
Publisher: WILEY C
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Chapter 40, Problem 31P
To determine
To find:
(a) the highest occupied sub-shell for Selenium.
(b) the number of electrons in the highest occupied sub-shell for Selenium.
(c) the highest occupied sub-shell for Bromine.
(d) the number of electrons in the highest occupied sub-shell for Bromine.
(e) the highest occupied sub-shell for Krypton.
(f) the number of electrons in the highest occupied sub-shell for Krypton.
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Consider the elements selenium (Z = 34), bromine (Z = 35), and krypton (Z = 36). In their part of the periodic table, the subshells of the electronic states are filled in the sequence 1s 2s 2p 3s 3p 3d 4s 4p . . . . What are (a) the highest occupied subshell for selenium and (b) the number of electrons in it, (c) the highest occupied subshell for bromine and (d) the number of electrons in it, and (e) the highest occupied subshell for krypton and (f) the number of electrons in it?
Angular momentum and Spin. An electron in an H-atom has orbital angular momentum magnitude and
z-component given by
LĀ² = 1(1+1)ħĀ², 1 = 0,1,2,..., n-1
Lz = māħ,
mā = 0, Ā±1, Ā±2,..., Ā±l
3
SĀ² = s(s+1)hĀ² = hĀ²,
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 = VĀ²/V
The electronic structure of one-dimensional chain of sodium (Na) atoms can be
approximately described by the particle-in-a-box model. The energy of each state can
be calculated using
nĀ²h?
En =
5,n = 1,2,3, ...
8mL2
where L is the length of the 1D chain. Assuming L = ao(N ā 1), where N is the
number of Na atoms and ao = 0.360 nm is the internuclear distance.
a) Determine the energy gap between the highest occupied energy level and the
lowest unoccupied energy level as a function of N. Assume that N is an even number
that is large enough
Chapter 40 Solutions
FUND OF PHYSICS VOL 1-W/WILEYPLUS >IC<
Ch. 40 - Prob. 1QCh. 40 - Prob. 2QCh. 40 - Prob. 3QCh. 40 - Prob. 4QCh. 40 - Prob. 5QCh. 40 - Prob. 6QCh. 40 - Prob. 7QCh. 40 - Figure 40-22 shows three points at which a spin-up...Ch. 40 - Prob. 9QCh. 40 - Prob. 10Q
Ch. 40 - Prob. 11QCh. 40 - Prob. 12QCh. 40 - Prob. 13QCh. 40 - Prob. 14QCh. 40 - Prob. 1PCh. 40 - Prob. 2PCh. 40 - Prob. 3PCh. 40 - Prob. 4PCh. 40 - Prob. 5PCh. 40 - Prob. 6PCh. 40 - Prob. 7PCh. 40 - Prob. 8PCh. 40 - Prob. 9PCh. 40 - Prob. 10PCh. 40 - Prob. 11PCh. 40 - Prob. 12PCh. 40 - SSM What is the acceleration of a silver atom as...Ch. 40 - Prob. 14PCh. 40 - Prob. 15PCh. 40 - Assume that in the SternGerlach experiment as...Ch. 40 - Prob. 17PCh. 40 - Prob. 18PCh. 40 - Prob. 19PCh. 40 - Prob. 20PCh. 40 - Prob. 21PCh. 40 - Prob. 22PCh. 40 - Prob. 23PCh. 40 - Prob. 24PCh. 40 - Prob. 25PCh. 40 - Prob. 26PCh. 40 - Prob. 27PCh. 40 - Show that the number of states with the same...Ch. 40 - Prob. 29PCh. 40 - For a helium atom in its ground state, what are...Ch. 40 - Prob. 31PCh. 40 - Prob. 32PCh. 40 - Prob. 33PCh. 40 - Prob. 34PCh. 40 - Prob. 35PCh. 40 - Prob. 36PCh. 40 - Prob. 37PCh. 40 - Prob. 38PCh. 40 - Prob. 39PCh. 40 - Prob. 40PCh. 40 - Prob. 41PCh. 40 - Prob. 42PCh. 40 - Prob. 43PCh. 40 - Prob. 44PCh. 40 - Prob. 45PCh. 40 - Prob. 46PCh. 40 - Prob. 47PCh. 40 - Prob. 48PCh. 40 - Prob. 49PCh. 40 - Prob. 50PCh. 40 - Prob. 51PCh. 40 - Prob. 52PCh. 40 - Prob. 53PCh. 40 - Prob. 54PCh. 40 - Prob. 55PCh. 40 - Prob. 56PCh. 40 - Prob. 57PCh. 40 - Prob. 58PCh. 40 - Prob. 59PCh. 40 - Prob. 60PCh. 40 - Prob. 61PCh. 40 - Prob. 62PCh. 40 - Prob. 63PCh. 40 - Prob. 64PCh. 40 - Prob. 65PCh. 40 - Prob. 66PCh. 40 - Prob. 67PCh. 40 - Prob. 68PCh. 40 - Prob. 69PCh. 40 - Prob. 70PCh. 40 - Prob. 71PCh. 40 - Prob. 72PCh. 40 - Prob. 73PCh. 40 - Prob. 74PCh. 40 - Prob. 75PCh. 40 - Prob. 76PCh. 40 - Prob. 77PCh. 40 - Prob. 78PCh. 40 - Prob. 79P
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- For a hydrogen atom in an excited state with principal quantum number n, show that the smallest angle that the orbital angular momentum vector can make with respect to the z-axis is =cos1( n1n) .arrow_forwardYou are working on determining the angle that separates two hybridized orbitals. In the process of determining the coefficients in front of the various atomic orbitals, you align the first one along the z-axis and the second in the x/z-plane (so o = 0). The second hybridized orbital was determined to be: W2 = R1s + R2p, sin 0 + R2p, cos 0 Determine the angle, 0, in degrees to one decimal place (XX.X) that separates these two orbitals. Assume that the angle will be between 0 and 90 degrees.arrow_forwardAngular momentum and Spin. An electron in an H-atom has orbital angular momentum magnitude and z-component given by LĀ² = 1(1+1)ħĀ², Lz = māh, 1 = 0,1,2,..., n 1 - mā = 0, Ā±1, Ā±2, ..., Ā±l 3 SĀ² = s(s+1) hĀ² = =hĀ²ā 4 Consider an excited electron (n > 1) on an H-atom. The total angular momentum ] = L + Å , whose magnitude and z-component follow a similar dependence to some quantum numbers j and m; as JĀ² = j(j + 1)ħĀ², Jz = mjħ 1 Sā = māh = Ā± = h Where j and m; are quantum numbers which assume values that jumps in steps of one such that j is non-negative and āj ā¤ mĀ” ā¤ 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.arrow_forward
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- If elements beyond Z = 120 are ever synthesized, electrons in these heavy atoms will begin filling a g subshell, corresponding to l = 4. How many states will be in a g subshell?arrow_forwardAn electron occupying the n = 6 shell of an atom carries z-component orbital angular momentum = (ā2) Ć h/2Ļ. Given that the electronās total orbital angular momentum is x Ć h/2Ļ, what is the minimum possible value of number x(remember to use the scientific notation)?arrow_forwardZirconium (Z= 40) has two electrons in an incomplete d sub- shell. (a) What are the values of n and e for each electron? (b) What are all possible values of me and m? (c) What is the electron configuration in the ground state of zirconium?arrow_forward
- (a) The doubly charged ion N2+ is formed by removing two electrons from a nitrogen atom. What is the ground-state electron configuration for the N2+ ion? (b) Estimate the energy of the least strongly bound level in the L shell of N2+. (c) The doubly charged ion P2+ is formed by removing two electrons from a phosphorus atom. What is the ground-state electron configuration for the P2+ ion? (d) Estimate the energy of the least strongly bound level in the M shell of P2+arrow_forwardWhat is the full electron configuration in the groundstate for elements with Z equal to (a) 26, (b) 34, (c) 38?arrow_forwardH-atom. The wave function of one of the electrons in the 2p orbital is given by (ignoring spin) r 2,1,0 (1,0,0)= - 7 exp(-270) c ao 1 |32ĻĪ± cose Where do is the Bohr radius. In the Bohr model, the radius of the electron orbit is given by m=2 = nĀ²ao = 4ao. The probability that the electron can be found at some radius between r and r + dr is given by 2Ļ P(r) dr = ā2 = ā āĀ²ĀŖ d$ S Ā² What is the expectation value of the distance of the electron from the nucleus (r)? Clue: expected value is computed by (r) = forP(r) dr then do integration by parts do sin 0 de | Yn.l.mĀ² (r, $,0)|Ā²rĀ² drarrow_forward
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