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Chapter 36: Problem 55

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 maximum orbital angular momentum that can be added without changing its principal quantum number is \(3 ħ\), and the new state would be \(6h\).

Step by step solution

01

Analyze Quantum Numbers

The electron is in the \(6d\) state, which means that the principal quantum number \(n = 6\) and the electron is in a 'd' orbital. The letter 'd' corresponds to the orbital quantum number \(l = 2\).
02

Determine Quantum Number Restrictions

The maximum possible value of the orbital quantum number \(l\) for a given principal quantum number \(n\) is \(n - 1\). Therefore, in this case, the maximum possible value for \(l\) is \(6 - 1 = 5\).
03

Calculate Change in Orbital Angular Momentum

Going from \(l = 2\) to \(l = 5\), we have an increase of \(5 - 2 = 3\) units in the orbital angular momentum. Each unit of \(l\) corresponds to \( ħ \) in angular momentum. Therefore, this represents a \( 3 ħ \) increase in the angular momentum.
04

Identify New Electron State

With the increase in orbital angular momentum, the electron state changes from 'd' to 'h'. This is because the letter 'h' represents the orbital quantum number 5. So, the new electron state is \(6h\).

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Most popular questions from this chapter

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