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Chapter 3: Problem 77

Explain why that if \(n=2, l\) cannot be 2

Short Answer

Expert verified
In Quantum Mechanics, the azimuthal quantum number \(l\) can take any integer value from 0 to \(n-1\). Therefore, if \(n=2\), \(l\) cannot be 2 as the possible values for \(l\) are only 0 and 1.

Step by step solution

01

Understanding quantum numbers

In Quantum Mechanics, the principal quantum number (n) represents the main energy level of an electron in an atom. It is always a positive integer. The azimuthal quantum number (l), defines the shape of the electron's orbital. l can take any integer value from 0 to n-1.
02

Applying definitions to our problem

Given our principal quantum number n=2, we need to find the possible values of l. Since l can take any integer values from 0 to (n-1), the possible values of l when n=2 would be 0 and 1.
03

Drawing Conclusion

Based on the definitions and our calculations, we can conclude that if n=2, l cannot be equal to 2 since the maximum possible value for l is 1 when n=2. Thus, the statement is correct regarding Quantum Mechanics rules.

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