Quantum numbers arise naturally from the mathematics used to describe the possib

Question

Quantum numbers arise naturally from the mathematics used to describe the possible states of an electron in an atom. The four quantum numbers, the principal quantum number (n), the angular momentum quantum number (), the magnetic quantum number (m), and the spin quantum number (ms) have strict rules which govern the possible values. Identify allowable combinations of quantum numbers for an electron. Select all that apply.

Quantum numbers arise naturally from the mathematics used to describe the possible states of an electron in an atom. The four quantum numbers, the principal quantum number (n), the angular momentum quantum number (l), the magnetic quantum number (me), and the spin quantum number (ms) have strict rules which govern the possible values Identify allowable combinations of quantum numbers for an electron Select all that apply. n 3, t 2, me 0, m 1/2 n 4, 1, m 2, ms E +1/2 n 1, t 1, m 0, m +1/2 n E 5, t 1, me 0, ms +1/2 n F 3, t 2, me E 0, m. +1/2 n 2, 0, me 0, ms- 1

Explanation / Answer

n is the principal quantum number with values n = 1,2,3....

l is the azimuthal quantum number with values ranging from 0 to n-1,ml is the magnetic quantum number with values ranging from -l to +l,and ms is the spin quantum number with values +1/2 and -1/2.

Lets find out now whether the combinations are allowable are not.

1.n =3,l=2,ml =0,ms=-1/2

n =3

Possible values of l,

l=0 to n-1 = 0,1,2

Possible values for ml,

ml = -l to +l = -2,-1,0,1,2

ms = -1/2,+1/2

So,allowable combination.

2.n =4,l=1,ml =2,ms=+1/2

Possible values-

n=4

l = 0 to n-1 = 0,1,2,3

ml = -l to +l = -3,-2,-1,0,1,2,3

ms = +1/2,-1/2

Thus,allowable combination.

3.n=1,l=1,ml=0,ms=+1/2

Possible values-

n=1

l=0

ml = 0

ms = +1/2,-1/2

Thus l=1 not possible.

So not an allowable combination.

4.n=5,l=1,ml=0,mS=+1/2

Possible values-

n=5,

l= 0,1,2,3,4

ml = -4,-3,-2,-1,0,1,2,3,4

ms = -1/2,+1/2

Allowable Combination.

5.n=3,l=-2,ml=0,ms=+1/2

Possible values-

n=3,

l=0,1,2

ml= -2,-1,01,2

ms = -1/2,+1/2

Thus l=-2 not possible

So,not possible combination

6. n=2,l=0,ml=0,ms=1

n=2

l = 0,1

ml=-1,0,1

ms = -1/2,+1/2

Thus ms = 1 not possible

So not a possible combination.

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