Question

If the angular momentum of an electron in the second orbit of a hydrogen atom is \(J\), then the angular momentum of an electron in the third excited state of hydrogen is:

• A. \(2J\)
• B. \(3J\)
• C. \(4J\)
• D. \(6J\)

Hint:

The principal quantum number directly influences the angular momentum of an electron in a hydrogen atom. Each increase in quantum number \( n \) increases the angular momentum proportionally.

Answer 1

The Correct Option is A

Step 1: Understand the relationship between angular momentum and quantum numbers in hydrogen. Angular momentum \( L \) of an electron in an orbit is quantized and given by \( L = n\hbar \), where \( n \) is the principal quantum number. 
Step 2: Apply the relationship to the given orbits. The second orbit corresponds to \( n=2 \) and the third excited state corresponds to \( n=4 \) (since the ground state is \( n=1 \), first excited state is \( n=2 \), second excited state is \( n=3 \), and the third excited state is \( n=4 \)). \[ L_{n=4} = 4\hbar = 2 \times (2\hbar) = 2J. \] Here \( 2\hbar \) corresponds to the angular momentum at \( n=2 \), which we're given as \( J \).