Question

Identify which sets of Quantum Numbers are valid for an electron. Each set is ordered (n,ℓ,mℓ,ms).

Answer 1

These are the rules of the quantum numbers that you have to use to dilucidate the validity of a set of quantum numbers:


1) Main quantum number, n: 1, 2, 3, 4, 5, 6, 7


2) Second quantum number, ℓ: 0, 1, 2, ... n-1


3) Third quantum number (magnetic quantum number), mℓ: -l,...0,,,,+l


4) Fourth quantum number (spin): ms: +1/2 or -1/2


Answers:

i) 3,2,0,1/2: valid, because 0<= l < n; - l <= ml <= +l; and ms = +1/2 or -1/2


ii) 2,2,-1, 1/2 invalid because l = n (violates second rule)

iii) 4,3,-4,1/2 invalid because ml is less than - l (violates third rule)

iv) 1,0,0,1/2 valid: meet the four rules

v) 2,2,1,-1/2 invalid because l = n (violate the second rule)

vi) 3,2,1,1 invalid because ms can be only +1/2 or -1/2 (fourth rule)


vii) 0,1,1,-1/2 invalid because l > n (violates rule 2)


viii) 3,3,1,1/2 invalid because l = n (violate rule 2)


ix) 2,-2,-2,-1/2 invalid because l is negative (violates rule 2)


x) 3,2,2,1/2 valid: meet the four rules

xi) 4,2,1,1/2 valid: meet the four rules


xii) 2,1,-1,-1/2 valid meet the four rules

Answer 2

Further explanation

In an atom, there are energy levels in the shell and sub shell.

This energy level is expressed in terms of electron configurations.

Writing the electron configuration starts from the lowest to the highest subshell's energy level. There are 4 sub-shells in an atom's shell, namely s, p, d, and f. The maximum number of electrons for each subshell is

s: 2 electrons

p: 6 electrons

d: 10 electrons and

f: 14 electrons

Electron filling in subshells using the following sequence:

1s², 2s², 2p⁶, 3s², 3p⁶, 4s², 3d¹⁰, 4p⁶, 5s², 4d¹⁰, 5p⁶, 6s², etc.

Each sub-shell also has orbitals drawn in the form of a square box in which there are electrons symbolized by half arrows.

Each orbital in an atom consists of 4 quantum numbers

n is the principal quantum number.

l is the angular momentum / azimuthal quantum number

ml, the magnetic quantum number

ms, the electron-spin quantum number

Value of n: positive integer

value of l: s = 0, p = 1, d = 2, f = 3 , ..(n-1)

ml value: between -l to + l

ms value: +1/2 or -1/2

• 1. 3,2,0,1/2 : valid

n = 3

l = 2 = d

ms = -2,-1,0,1,2

ml = +1/2 or -1/2

• 2. 2,2,-1, 1/2 : invalid

n = 2

l = 2 >>>the maximum value is at n-1

• 3. 4,3,-4,1/2 : invalid

n = 4

l = 3

ml = -3,-2,-1,0,1,2,3 >>> there is no -4

ms = +1/2 or -1/2

• 4. 1,0,0,1/2 : valid

n = 1

l = 0

ml = 0

ms = +1/2 or -1/2

• 5. 2,2,1,-1/2 : invalid

n = 2

l = 2 >>> l must be n-1

• 6. 3,2,1,1 : invalid

n = 3

l = 2

ms = -2,-1,0,1,2

ml = +1/2 or -1/2  >>>  there is no 1

• 7. 0,1,1,-1/2 : invalid

n = 0 >>> there is no n = 0, it starts from 1

• 8. 3,3,1,1/2 : invalid

n = 3

l = 3 >>>the maximum value is at n-1

• 9. 2,-2,-2,-1/2 : invalid

n = 2

l = -2 >>> no negative value for l

• 10. 3,2,2,1/2 : valid

n = 3,

l = 2

ml = -2,-1,0,1,2

ms = +1/2 or -1/2

• 11. 4,2,1,1/2 : valid

n = 4

l = 2

ml = -2,-1,0,1,2

ms = ms = +1/2 or -1/2

• 12. 2,1,-1,-1/2 : valid

n = 2

l = 1

ml = -1,0,1

ms = +1/2 or -1/2

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Keywords: orbitals, subshells, quantum numbers