Explanation Given: 1875 nm 1282 nm 1093 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 lo = 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 nm = 1×10 -9 m 1875 nm × 1×10 -9 m 1 nm =1875×10 -9 m ν = c λ ν = 2 .998 × 10 8 m /s 1875×10 -9 m ν = 1 .6 × 10 14 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 ) 1 .6 × 10 14 s − 1 = 2 .180×10 -18 J 6 .626 ×10 -34 J×s ( 1 3 2 - 1 n hi 2 ) 1 9 - 1 n hi 2 = 1 .6 × 10 14 s − 1 × 6 .626 ×10 -34 J × s 2 .180×10 -18 J 0 .1111- 1 n hi 2 =4 .86 ×10 -2 1 n hi 2 =0 .111-4 .86 ×10 -2 1 n hi 2 =0 .0624 n hi 2 = 1 0 .0624 n hi 2 =16 n hi =4 The transition starts from n hi = 4 , and occurred 4 → 3 b. First, we will convert wavelength in meters: 1 nm = 1×10 -9 m 1282 nm × 1×10 -9 m 1 nm =1282×10 -9 m ν = c λ ν = 2 .998 × 10 8 m /s 1282×10 -9 m ν = 2 .34 × 10 14 s -1 The frequency is 2.34 × 10 14 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 ...

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ISBN: 9780133888584

Author: Tro

Publisher: VST

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Quantum Chemistry

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Chapter 3, Problem 83E

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Assign given wavelengths to transition in the hydrogen atom

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Chapter 3, Problem 82E

Chapter 3, Problem 84E

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Assign 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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Chapter 3 Solutions

To determine:

Assign given wavelengths to transition in the hydrogen atom