Question

What is the angular momentum of an electron in the 4th stationary state of hydrogen atom? (\(h=6.626\times 10^{-34}\) Js)

• A. \(4.22\times 10^{-34}\) JS
• B. \(2.6504\times 10^{-34}\) JS
• C. \(3.313\times 10^{-34}\) JS
• D. \(1.325\times 10^{-34}\) JS

Hint:

Use Bohr's quantisation rule L = n h / (2 pi) with n = 4.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
Bohr's postulate gives the angular momentum of the electron in the \(n\)-th orbit as \(L=\dfrac{nh}{2\pi}\).

Step 2: Calculation
For the 4th state \(n=4\):
\(L=\dfrac{4\times 6.626\times 10^{-34}}{2\times 3.14}\)
\(L=\dfrac{26.504\times 10^{-34}}{6.28}\approx 4.22\times 10^{-34}\) J s

Step 3: Compare the options
This matches option (A).

Final Answer:
The angular momentum is about 4.22e-34 J s. \[ \boxed{\text{(A) }4.22\times 10^{-34}\text{ Js}} \]