Show that the radial probability density for the ground state of the hydrogen atom has maximum at r = a.

Explanation

To show that the radial probability density for the ground state of the hydrogen atom has a maximum at \( r = a \), we will follow these steps:

### Step 1: Write the expression for the radial probability density
The radial probability density \( P(r) \) for the ground state of the hydrogen atom is given by:
\[ P(r) = \frac{8}{a^3} r^2 e^{-2r/a} \]
where \( a \) is the Bohr radius.
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