J.R. S. answered • 10/30/22
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1 / λ = RH (1/n12 - 1/n22)
λ = wavelength in meters = 92.3x10-9 m
RH = 1.0973x107 m-1
n1 = ground state = 1
n2 = final state = ?
1 / 92.3x10-9 m = 1.0973x107 m-1 (1 - 1/x2)
1.08x107 m = 1.0973x107 m-1 - 1.0973x107 m-1 / x2
173,000 = 1.0973x107 m-1 / x2
x = 8
So, the final state of the hydrogen atom would be n = 8
J.R. S.
tutor
Excuse me??? By nf, I assume you mean n(final). If that's the case, the nf would be n=8 according to my calculations. If the match is wrong, I apologize. Do the math and see what you get.
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10/30/22
Nina Z.
I tried it out, the answer is 9 The energy of a photon, 𝐸, can be determined from the wavelength via the equation 𝐸=ℎ𝑐𝜆 where ℎ is Planck's constant and 𝑐 is the speed of light. First, convert the wavelength from nanometers to meters. 92.3 nm×1 m109 nm=92.3×10−9 m The energy for a photon of wavelength 92.3 nm is 𝐸=ℎ𝑐𝜆=(6.626×10−34 J⋅ s)(2.998×108 m⋅ s−1)92.3×10−9 m=2.15×10−18 J Use the Rydberg equation that relates the energy, 𝐸, of the photon with the initial ground state, 𝑛i=1, and the final state, 𝑛f. The final state is unknown. 𝐸=2.15×10−18 J=2.1799×10−18 J(112−1𝑛2f) This yields 0.988𝑛2f𝑛f=1−1𝑛2f=81=9
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11/05/22
J.R. S.
tutor
E = hcλ? I think you mean E = hc / λ. I'm assuming your calculations are correct, which would mean mine are incorrect. I re-did my calculations and find n(final) = 8.9 = 9, so I do agree with your calculations. My method is a correct one, I simply made a math error. If the OP had bothered to run through the calculations as I have them outlined, he/she would have arrived at the correct answer of n(final) = 9. Sad, but true. Learn a lesson from this Baran M.
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11/05/22
Baran M.
wrong. what is nf?10/30/22