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Chapter 36: Problem 61

What's the most orbital angular momentum that could be added to an atomic electron initially in the \(6 d\) state without changing its principal quantum number? What would be the new state?

Short Answer

Expert verified
The greatest possible orbital angular momentum that can be added to the electron without changing its principal quantum number is \(\sqrt{30}\hbar\), and the new state is \(6h\).

Step by step solution

01

Identify Initial State

The electron's initial state is \(6d\) and its orbital quantum number (\(l\)) is 2 for the \(d\) state.
02

Change of Orbital Quantum Number (\(l\))

Increase the \(l\) value while keeping the principal quantum number (\(n\) = 6) the same. The next \(l\) values will be 3 for the \(f\) state, 4 for the \(g\) state, and 5 for the \(h\) state. The highest possible \(l\) value without changing the \(n\) value is 5 (\(h\) state).
03

Calculate the Orbital Angular Momentum

The formula for calculating the orbital angular momentum (\(L\)) is \(\sqrt{l(l + 1)}\hbar\). Replace \(l\) with 5 and calculate \(L\) to be \(\sqrt{5(5+1)}\hbar\) or \(\sqrt{30}\hbar\).

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