The ion ( ) has a state with radial wave function

PHYSICS · Multi-part · Fermi University Physics · Atomic, Molecular & Optical Physics · One-electron atoms and the origins of atomic structure · One-electron atoms and the origins of atomic structure

Reading the Spectrum, Ch Radial functions, orbital size and Rydberg states

Problem

The

\mathrm{He^+}

ion (

Z=2

) has a

2p_0

state with radial wave function

R_{21}\propto r\,e^{-Zr/2a_0}

, so

P(r)\propto r^4e^{-Zr/a_0}.

((a)) Find, in terms of

a_0

and

Z

, the radius at which

P(r)

is a maximum. ((b)) Evaluate this radius in nm for

\mathrm{He^+}

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