# 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=(mV

The balance of forces

(Ze

From here we get

E=-(Ze

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=(Ze

but as we know from atomic physics

hν=hcR(1/(n

E=(mV

^{2})/2-(Ze^{2})/(4πε_{0}r.) (1)The balance of forces

(Ze

^{2})/(4πε_{0}r^{2})=(mV^{2})/r (2)From here we get

E=-(Ze

^{2})/(8πε_{0}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=(Ze

^{4}m)/(32 ε_0^{2}π^{2}ħ^{2})(1/(n_{1}^{2})-1/(n_{2}^{2}))but as we know from atomic physics

hν=hcR(1/(n

_{1}^{2})-1/(n_{2}^{2}))**R = (Ze**^{4}m)/(32ε_{0}^{2}π^{2}ħ^{3}c) = 1.0974
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