Explanation Given: 121.5 nm 102.6 nm 97.23 nm Formula used: To calculate the energy level of transition of hydrogen atom use the following equation: ν= R H h ( 1 n lo 2 - 1 n hi 2 ) ν = frequency R H = Rydberg constant ( 2.180 × 10 − 18 J ) h = Planck constant (6 .626 × 10 − 34 J ⋅ s ) n Io = lowest level n hi = highest level ν = c λ ν = frequency, λ = Wave length, c = speed of light (2 .998 × 10 8 m / s ) Calculation: a. First, we will convert wavelength in meters: 1 n m = 1 × 10 − 9 m 121.5 n m × 1 × 10 − 9 m 1 n m = 121.5 × 10 − 9 m ν = c λ ν = 2.998 × 10 8 m / s 121.5 × 10 − 9 m ν = 2 .5 × 10 15 s − 1 Now we will calculate the energy level of transition of hydrogen atom use the following equation: ν = R H h ( 1 n lo 2 − 1 n hi 2 ) 2.5 × 10 15 s − 1 = 2.180 × 10 − 18 J 6.626 × 10 − 34 J ⋅ s ( 1 1 2 − 1 n h i 2 ) 1 1 − 1 n h i 2 = 2.5 × 10 15 s − 1 × 6.626 × 10 − 34 J ⋅ s 2.180 × 10 − 18 J 1.00 − 1 n h i 2 = 7.6 × 10 − 1 1 n hi 2 = 1.00 − 0.76 1 n hi 2 = 0.24 n hi 2 = 1 0.24 n hi 2 = 4 n hi = 2 The transition starts from n hi = 2 , and occurred 2 → 1 b. First, we will convert wavelength in meters: 1 n m = 1 × 10 − 9 m 102.6 n m × 1 × 10 − 9 m 1 n m = 102.6 × 10 − 9 m ν = c λ ν = 2.998 × 10 8 m / s 102.6 × 10 − 9 m ν = 3 .0 × 10 15 s − 1 Now we will calculate the energy level of transition of hydrogen atom use the following equation: ν = R H h ( 1 n lo 2 − 1 n hi 2 ) 3 ...

Chemistry: Structure and Properties (2nd Edition)

2nd Edition

ISBN: 9780134293936

Author: Nivaldo J. Tro

Publisher: PEARSON

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Quantum Chemistry

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Chapter 2, Problem 84E

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Assign the given wavelengths to transition in the hydrogen atom

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Chapter 2, Problem 83E

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Assign the given wavelengths to transition in the hydrogen atom

Solution Summary: The author explains how to calculate the energy level of transition of hydrogen atom using the following equation: R H h, Rydberg constant, Planck constant and speed of light.

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To determine:

Assign the given wavelengths to transition in the hydrogen atom