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Chapter 8: Problem 30

(a) How many angles can \(L\) make with the z-axis for an \(l=2\) electron? (b) Calculate the value of the smallest angle.

Short Answer

Expert verified
(a) An \(l=2\) electron can make 5 angles with the z-axis. (b) The value of the smallest angle is \(\pi/4\).

Step by step solution

01

Calculate Number of Angles

We use the quantum number of \(l=2\), then the number of angles an electron can make with the z-axis are given by: \(2l+1\) , which equals \(2(2)+1 = 5\).
02

Calculate the Range of Angles

In spherical coordinates, the range of the polar angle is from 0 to \(\pi\) which means the total range of the angle is \(\pi\).
03

Calculate the smallest angle

The smallest angle corresponds to the smallest variation in the electron orientations which would be the difference between the first and the second orientation. Since we have five different orientations, the step between these orientations should be \(\pi/(5-1) = \pi/4\) (since the five angles cover the full range of variation from 0 to \(\pi\)).

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