Interpretation Introduction To determine: The value of n for the level to which the electron gets relaxed in the hydrogen atom. Explanation Given: An electron of a hydrogen atom in the seventh level undergoes relaxation to lower energy level and emits a light of wavelength 397 nm . Explanation: The change in energy ( △ E ) that takes place during a transition in an atom is determined using the formula as follows: △ E = − 2.18 × 10 − 18 J ( 1 n f 2 − 1 n i 2 ) …… (1) Here, n i is the initial state and n f is the final state. Calculate △ E for the transition that takes place as follows: n = 7 → n = x Assume the lower level to which the electron gets relaxed in the hydrogen atom to be x . Substitute n i as 7 and n f as x in equation (1) as follows: △ E = − 2.18 × 10 − 18 J ( 1 x 2 − 1 7 2 ) = − 2.18 × 10 − 18 J ( 1 x 2 − 1 49 ) The negative sign shows the emission of energy. The relationship between the energy of the photon ( E ) and the wavelength is as follows: E = h c λ …… (2) Here, h is the Planck’s constant, c is the speed of light, and λ is the wavelength of light. The relation between the energy of photon and change in energy is as follows: E = − △ E Substitute △ E as − 2.18 × 10 − 18 J ( 1 x 2 − 1 49 ) in the above expression as follows: E = − ( − 2.18 × 10 − 18 J ( 1 x 2 − 1 49 ) ) = 2.18 × 10 − 18 J ( 1 x 2 − 1 49 ) Substitute the value of E from equation (2) in the above expression as follows: h c λ = 2

Chemistry: A Molecular Approach Selected Solutions Manual, Books a la Carte Edition

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ISBN: 9780134554259

Author: Nivaldo J. Tro

Publisher: PEARSON

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Chapter 7, Problem 71E

Interpretation Introduction

To determine: The value of n for the level to which the electron gets relaxed in the hydrogen atom.

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Chapter 7, Problem 70E

Chapter 7, Problem 72E

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Chapter 7 Solutions

Chemistry: A Molecular Approach Selected Solutions Manual, Books a la Carte Edition

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