# What is ΔE for the transition of an electron from n = 8 to n = 5 in a hydrogen atom? What is the frequency of the spectral line produced?

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- BrentLv 63 years agoFavorite Answer
E = -E0/n², where E0 = 13.6 eV (1 eV = 1.602×10^-19 J)

ΔE = (-13.6 eV)(1.602×10^-19 J) (1/5² - 1/8²)

= (-13.6 eV)(1.602×10^-19 J) (0.024375)

= - 5.31×10^-20 J

Answer is negative because energy is lost. The lost energy is transformed into a photon of electromagnetic energy. To find the wavelength, we need Planck's Constant

E = hf

5.31×10^-20 J = (6.626×10^-34 J/Hz) f

f = 8.01×10^13 Hz or 80.1 THz

This frequency is in the near infrared region just below visible light.

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