Explanation 1) Concept: We will use the relation between the energy and the wavelength. Using that, we will find out the energy associated with a particular wavelength λ , then by calculating the ground state energy, we can further calculate the energy of the first excited state. 2) Formula: i) ν = c / λ Here, c is the speed of light in the vacuum ii) E = h ν = h c λ where h is a Planck’s constant and ν is the frequency of spectral line iii) h c = 1240 e V 3) Given: i) Wavelength of absorbed spectral line1, λ a = 14.588 n m ii) Wavelength of absorbed spectral line2, λ b = 4.8437 n m iii) Cutoff wavelength below which no absorption possible is λ c = 2.9108 n m iv) E 4 = 450 e V 4) Calculations: We have the relation between energy and wavelength. Using that, we will find out the energy associated with a particular wavelength λ . E a = h c λ a = 1240 e V . n m 14.588 n m ≈ 85 e V E b = h c λ b = 1240 e V . n m 4.8437 n m ≈ 256 e V E c = h c λ c = 1240 e V

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ISBN: 9781118230725

Author: David Halliday, Robert Resnick, Jearl Walker

Publisher: Wiley, John & Sons, Incorporated

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The Bohr model

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Chapter 39, Problem 19P

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The energy of the first excited state of the electron

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Chapter 39 Solutions

Fundamentals of Physics Extended

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The energy of the first excited state of the electron

Solution Summary: The author explains the relation between energy and wavelength, and calculates the energy of the first excited state.

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To find: The energy of the first excited state of the electron

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Chapter 39 Solutions

To find:

The energy of the first excited state of the electron