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Answer to Question #2477 in Atomic and Nuclear Physics for berkan

Question #2477
Evaluate the Rydberg constant R using Bohr theory and show that its value is R = 1.0974x10-1.
Expert's answer
The energy of electron in atom
E=(mV2)/2-(Ze2)/(4πε0 r.) (1)

The balance of forces
(Ze2)/(4πε0 r2 )=(mV2)/r (2)

From here we get
E=-(Ze2)/(8πε0 r.) (3)

Multiplying (2) by mr^3 and using L=nħ we get
(Ze^2 mr)/(4πε_0 )=(mVr)^2=n^2 ħ^2

And finally
E=-(Ze^4 m)/(32 ε_0^2 π^2 n^2 ħ^2.)

Then
hν=(Ze4 m)/(32 ε_02 π2 ħ2 )(1/(n12 )-1/(n22 ))

but as we know from atomic physics

hν=hcR(1/(n12 )-1/(n22 ))

R = (Ze4 m)/(32ε02 π2 ħ3 c) = 1.0974

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