The orbital angular momentum of an electron in a 3s orbital is x h2. The value of x is (nearest integer).

Given: The orbital angular momentum of an electron in a 3s orbital is x h2. Find: The value of x. The orbital angular momentum is given by L = l(l+1)h2 For an s-orbital, l = 0. Substituting l = 0, L = 0(0+1)h2 = 0 Comparing with x h2, we get x = 0. Therefore, the value of x is 0.

The orbital angular momentum of an electron in a 3s orbital is x… — Solution | JEE Chemistry

NVAEasyJEE 2023Quantum Numbers

The orbital angular momentum of an electron in a $3s$ orbital is $\frac{x h}{2\pi}$ . The value of $x$ is _____ (nearest integer).

Answer

Correct answer:0

Step-by-step solution

Standard Method

Given: The orbital angular momentum of an electron in a $3s$ orbital is $\frac{x h}{2\pi}$ .

Find: The value of $x$ .

The orbital angular momentum is given by

L = \frac{\sqrt{l(l+1)}h}{2\pi}

For an $s$ -orbital, $l = 0$ . Substituting $l = 0$ ,

L = \frac{\sqrt{0(0+1)}h}{2\pi} = 0

Comparing with $\frac{x h}{2\pi}$ , we get $x = 0$ .

Therefore, the value of $x$ is $0$ .

Common mistakes

Taking the principal quantum number $n = 3$ as the angular momentum quantum number. This is wrong because orbital angular momentum depends on $l$ , not on $n$ . For a $3s$ orbital, use $l = 0$ .
Using the formula incorrectly as proportional to $l h/2\pi$ instead of $\sqrt{l(l+1)}h/2\pi$ . This gives incorrect values for orbital angular momentum. Always substitute into the correct quantum mechanical expression.

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