Answered: Use the Rydberg equation 1/λ=…

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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Question

Use the Rydberg equation 1/λ= R(a1/n₁²-1/n₂²) to calculate the wavelength (in Å)of the photon absorbed when a hydrogen atom undergoes a tran-sition from n=1 to n=3.

Expert Solution

Step 1

Rydberg equation is used to determine the wavelength of the photon absorbed when the electron goes in transition. The formula used to determine is

$\frac{1}{λ} = R (\frac{1}{{n_{1}}^{2}} - \frac{1}{{n_{2}}^{2}}) .$

Whereas,

R is Rydeberg constant(R=10968 cm^-1).

n₁ and n₂ are the numbers of shells in which transition takes place.

λ is the wavelength.

Step 2

To determine the wavelength of the photon absorbed.

n₁=1, n₂=3.

Using the Rydberg equation.

$\begin{array}{rcl} \frac{1}{λ} & = & R (\frac{1}{{n_{1}}^{2}} - \frac{1}{{n_{2}}^{2}}) {cm}^{- 1} . \\ \frac{1}{λ} & = & 109680 (\frac{1}{1^{2}} - \frac{1}{3^{2}}) {cm}^{- 1} . \\ \frac{1}{λ} & = & 109680 (\frac{1}{1} - \frac{1}{9}) {cm}^{- 1} . \\ \frac{1}{λ} & = & 109680 \times \frac{8}{9} . \\ \frac{1}{λ} & = & 97493.33 {cm}^{- 1} . \\ λ & = & 1.0257 \times 10^{- 5} cm . \end{array}$

Convert wavelength into angstrom from cm.

$λ = 1.0257 \times 10^{- 5} cm \times \frac{10^{8} A^{o}}{1 cm} . λ = 1.0257 \times 10^{3} A^{o} or 1025.7 A^{o} .$

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