What must be the width of a one-dimensional infinite potential well if an electron trapped in it in the n =3 state is to have an energy of 4.7 eV?

Explanation

To solve the problem of finding the width of a one-dimensional infinite potential well for an electron in the n = 3 state with an energy of 4.7 eV, we will follow these steps:

### Step 1: Understand the formula for energy in a potential well
The energy of an electron in the n-th state of a one-dimensional infinite potential well is given by the formula:
\[ E_n = \frac{n^2 h^2}{8 m L^2} \]
where:
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