Two circular hydrogen Rydberg states are compared

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

Two circular hydrogen Rydberg states are compared, one with

n = 30

l = 29

and one with

n = 60

l = 59

(a circular state has the maximum possible

l = n-1

). Using only the powers of

n

given by the Rydberg scaling laws: ((a)) State the factor by which the mean radius, the binding energy, the level spacing to the next

n

, and the ionising field change when

n

is doubled from

30

60

. ((b)) Calculate the mean radius, the binding energy, the exact spacing to

n=61

(the positive difference

E_{61}-E_{60}

), and the ionising field of the

n = 60

l = 59

state, using

a_0 = 0.052918\,\mathrm{nm}

R_{\rm H} = 109677.58\,\mathrm{cm^{-1}}

, and the nuclear-field estimate of the ionising field,

F_{\rm ion} \approx 5.14\times10^9/n^4\,\mathrm{V\,cm^{-1}}

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