Question

write four quantum numbers for (a)1s1 (b)2p1 (c)3d1 (d)4f1

Answer 1

a. n=1 , l=0 ,m=0 ,s=+or -1/2
b.n=2 , l=1 ,m= -1 to 1 , s=+or-1/2
c.n=3 , l=2 , m=-2to 2,s=+or-1/2
d.n=4, l=3 , m=-3to 3,s=+or -1/2

Answer 2

Quantum Numbers:

• Quantum numbers are a set of numbers that gives the position and energy of a particular electron within an atom.
• Each electron has four quantum numbers associated with it that describe its state.
• The four quantum numbers are principal quantum number, azimuthal quantum number, magnetic quantum number, and spin quantum number.

Principal Quantum Number:

• The principal quantum number gives the level of the electronic shell.
• It is denoted as n and can have any non-zero positive value.
• n = 1, 2, 3, 4 for the s, p, d, and f orbital respectively.

Azimuthal Quantum Number:

• Azimuthal quantum number gives the shape of an orbital.
• It also gives the orbital angular momentum of the atomic orbital.
• It is denoted as l and can have vales starting from zero up to (n-1).
• For s orbital, l = 0; for p orbital, l = 0, 1; for d orbital, l = 0, 1, 2; for f orbital, l = 0, 1, 2, 3 and so on

Magnetic Quantum Number:

• The magnetic quantum number gives the orientation of a given orbital in space.
• It is denoted as $m_{l}$ and can have values from -l to +l through zero.
• for s orbital,  $m_{l}$ = 0; for p orbital, $m_{l}$ = -1, 0, +1; for d orbital, $m_{l}$ = -2, -1, 0, 1, 2; for f orbital, $m_{l}$ = -3, -2, -1, 0, 1, 2, 3 and so on.

Spin Quantum Number:

• The spin quantum number gives the angular momentum of an electron.
• As angular momentum is a vector, the spin quantum number has both direction as well as magnitude.
• It is denoted as  $m_{s}$ and can have a value of either +1/2 or -1/2.

Explanation:

(a) $1s^{1}$

Principal quantum number (n) = 1

Azimuthal quantum number (l) = 0

Magnetic quantum number ( $m_{l}$) = 0

Spin quantum number ( $m_{s}$) = +1/2 or -1/2

(b) $2p^{1}$

Principal quantum number (n) = 2

Azimuthal quantum number (l) = 1

Magnetic quantum number ( $m_{l}$) = -1

Spin quantum number ( $m_{s}$) = +1/2 or -1/2

(c) $3d^{1}$

Principal quantum number (n) = 3

Azimuthal quantum number (l) = 2

Magnetic quantum number ( $m_{l}$) = -2

Spin quantum number ( $m_{s}$) = +1/2 or -1/2

(d) $4f^{1}$

Principal quantum number (n) = 4

Azimuthal quantum number (l) = 3

Magnetic quantum number ( $m_{l}$) = -3

Spin quantum number ( $m_{s}$) = +1/2 or -1/2

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