Question

Quantum numbers arise naturally from the mathematics used to describe the possible states of an electron in an atom. The fourquantum numbers, the principal quantum number (n), the angular momentum quantum number (), the magnetic quantumnumber (me), and the spin quantum number (m₂) have strict rules which govern the possible values.Identify all allowable combinations of quantum numbers for an electron.On=1,= 1, me =□n=4, l=3, me =] n = 5,= 4, me =□n=2,= 0, me =-1, m, = -14, m, = -1/4, m₁ = -1/0, m, = 0Attemptsn = 3, e = 1, me = 1, m, = + 1/□n=3, = -1, me = 1, m, = -1

Answer 1

The correct possible combnations are:

n = 5, l = 4, ml = 4, ms = -1/2

n =3 l = 1, ml =1, ms = +1/2

Explanations:

For principal quantum numbers (n) are positive integers that is 1, 2, 3, ...

For angular quantum numbers, (l) the values only ranges from 0 to n - 1

The magnetic quantum numbers (ml) are integers that ranges from -l to +l

For spin quantum, numbers(me), the values can only be -1/2 or +1/2

• The, first option is wrong, becuase is n = 1, the ,value of l will be 0, (1 - 1)

,

• The ,second option is also not a correc,t combination since magnetic quantum numbers (ml) are only values from -3 to + 3 (4 exclusive)

• For the ,third combination,, when n = 5, l = (0, 1, 2, 3, 4), ml = (-4, 0, 1,2, 3, 4) and ms = -1/2 or +1/2

• Therefore the ,third combination is possible, since the given values are the set of numbers.

For the fourth combination

The fourth combination is not correct since the value of spin quantum number cannot be zero

For the fifth combination is also possible since all the number are within range.

The sixth combination is not possible since the value of angular quantum numbers, (l) cannot be -1