The probability distribution function (PDF) as a function of radial distance (r)

Question

The probability distribution function (PDF) as a function of radial distance (r) from the nucleus for an electron in the lowest energy state of a hydrogen atom is given by: Name the famous constant a. Show that this is a properly normalized PDF. Find the mode radius (most probable radial distance). Express as a multiple of the constant a. Find the mean radius (as a multiple of the constant a). Work with the rationalized variable u. Show throughout the use of the following definite integral. I_n = integral_0^infinity u^n e^-cu du = n!/C^n+1 (for positive integer n, positive real c)

Explanation / Answer

2. a) The constant a is known as Bohr's radius. Its the mean radius of the orbit of an electron of hydrogen atom at the ground state. Its value is 5.29 * 10-11 m.

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