Question

How many orbitals in an atom can have each of the following designations: (a) 1s; (b) 4d; (c) 3p; (d) n = 3?

Answer 1

Answer :

(a) Number of orbitals in an atom = 1

(b) Number of orbitals in an atom = 5

(c) Number of orbitals in an atom = 3

(d) Number of orbitals in an atom = 9

Explanation :

Principle Quantum Numbers : It describes the size of the orbital. It is represented by n. n = 1,2,3,4....

Azimuthal Quantum Number : It describes the shape of the orbital. It is represented as 'l'. The value of l ranges from 0 to (n-1). For l = 0,1,2,3... the orbitals are s, p, d, f...

Magnetic Quantum Number : It describes the orientation of the orbitals. It is represented as $m_l$. The value of this quantum number ranges from $(-l\text{ to }+l)$. When l = 2, the value of

Spin Quantum number : It describes the direction of electron spin. This is represented as $m_s$. The value of this is $+\frac{1}{2}$ for upward spin and $-\frac{1}{2}$ for downward spin.

Number of orbitals in an atom = (2l+1)

(a) 1s

n = 1

The value of 'l' for 's' orbital is, l = 0

Number of orbitals in an atom = (2l+1) = (2×0+1) = 1

(b) 4d

n = 4

The value of 'l' for 'd' orbital is, l = 2

Number of orbitals in an atom = (2l+1) = (2×2+1) = 5

(c) 3p

n = 1

The value of 'l' for 'p' orbital is, l = 1

Number of orbitals in an atom = (2l+1) = (2×1+1) = 3

(a) n = 3

l = 0, 1, 2

Number of orbitals for (l = 0) = (2l+1) = (2×0+1) = 1

Number of orbitals for (l = 1) = (2l+1) = (2×1+1) = 3

Number of orbitals for (l = 2) = (2l+1) = (2×2+1) = 5

Number of orbitals in an atom = 1 + 3 + 5 = 9