Part A
How many different values of l are possible for an
electron with principal quantum number n = 2?
Express your answer as an integer.
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Part B
How many values of
ml are possible for an electron with
orbital quantum number
l = 1?
Express your answer as an integer.
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Part C
The quantum state of a particle can be specified by giving a
complete set of quantum numbers (
n,
l,
ml,
ms). How many different
quantum states are possible if the principal quantum number is
n = 5?
To find the total number of allowed states, first write down the
allowed orbital quantum numbers
l, and then write down the
number of allowed values of
ml for each orbital quantum
number. Sum these quantities, and then multiply by 2 to account for
the two possible orientations of spin.
Express your answer as an integer.
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Part
Part D
Is the state
n=3,
l=3,
ml=−2,
ms=1/2 an allowable
state? If not, why not?
Is the state , , , an allowable state? If not, why
not?
Yes it is an allowable state. |
No: The orbital quantum number cannot equal the principal
quantum number. |
No: The magnetic quantum number cannot be negative. |
No: The magnetic quantum number must equal the orbital quantum
number. |
No: The magnetic quantum number must equal the principal
quantum number. |
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Part E
What is the maximum angular momentum
Lmax that an
electron with principal quantum number
n = 3 can have?
Express your answer in units of ℏ. (You don’t need to enter the
ℏ, it is in the units field for you.)
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Part
Answer
Number symbols possible values 1) principle quantum numbers n 1, 2, 3, 4, . . . . 11) Angular momentum quantum no l 0, 1, 2 3, . . (n – 1) 111) magnetic quantum numbers ml – l, . . . . – 1, 0, 1, .. l 1v) spin quantum numbers ms + 1/2, – 1/ 2 so now A) for n = 2 possible value of l are 0, 1, 2 . . (n – 1) that is 0, 1 so, different value of l is 2 B) ml for l = 1, positive value of ml are – l, . . . . , – 1, 0, 1, ….l that is – 1, 0, 1 so different values possible for me is 3 for n = 5 l can be 0, 1, 3, 4 possible value of ml value are: (- l to l) for l = 0: ml: 0 l = 1: ml: – 1, 0, 1 l = 2: ml: – 2, – 1, 0, 1, 2 l = 3: ml: – 3, – 2, – 1, 0, 1, 2, 3 l = 4: ml: – 4, – 3, – 2, – 1, 0 1, 2, 3, 4 so that possible ml value are = 1 + 3 + 5 + 7 + 9