Calculate the radial probability density P(r) for the hydro- gen atom in its ground state at (a) r = 0, (b) r = a, and (c) r= 2a, where a is the Bohr radius.

Explanation

To calculate the radial probability density \( P(r) \) for the hydrogen atom in its ground state, we will use the formula:

\[ P(r) = \frac{4}{a^3} r^2 e^{-\frac{2r}{a}} \]

where \( a \) is the Bohr radius. We will evaluate this expression at three different values of \( r \): \( r = 0 \), \( r = a \), and \( r = 2a \).

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