Answered: Calculate the wavelength, in…

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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Part 1: Calculate the wavelength, in nanometers, for the colored line that appears in the spectrum of the hydrogen atom corresponding to an n=4 to n= 2 electronic transmission. The hydrogen atom emits visible light at the following wavelengths (given in nanometers with corresponding colors): 410 (violet), 434 (blue), 486 (green), and 656 (red). Part 2: Draw a simple energy level diagram for the hydrogen atom, and illustrate with arrows the transitions that give rise to VISIBLE light emissions.

Expert Solution

Step 1

Wavelength can be calculated using the equation:

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

R = Rydberg constant = 109677 cm^-1

n₁ = 4

n₂ = 2

$\frac{1}{λ} = 1.09 * 10^{7} m^{- 1} (\frac{1}{2^{2}} - \frac{1}{4^{2}}) = 1.09 * 10^{7} m^{- 1} (\frac{1}{4} - \frac{1}{16})$

= 2043750 m^-1

= 2.04 * 10⁶ m^-1

$λ = 4.90 * 10^{- 7} m$

= 490 * 10^-9 m

= 490 nm

Wavelength = 490 nm

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