   # One of the lines in the Balmer series of the hydrogen atom emission spectrum is at 397 nm. It results from a transition from an upper energy level to n = 2. What is the principal quantum number of the upper level? ### General Chemistry - Standalone boo...

11th Edition
Steven D. Gammon + 7 others
Publisher: Cengage Learning
ISBN: 9781305580343

#### Solutions

Chapter
Section ### General Chemistry - Standalone boo...

11th Edition
Steven D. Gammon + 7 others
Publisher: Cengage Learning
ISBN: 9781305580343
Chapter 7, Problem 7.81QP
Textbook Problem
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## One of the lines in the Balmer series of the hydrogen atom emission spectrum is at 397 nm. It results from a transition from an upper energy level to n = 2. What is the principal quantum number of the upper level?

Interpretation Introduction

Interpretation:

The principal quantum number of higher energy level in Balmer series of hydrogen atom emission spectrum at 397nm has to be identified.

Concept introduction:

Bohr developed a rule for quantization of energy that could be applicable to the electron of an atom in motion.  By using this he derived a formula for energy levels of electron in H-atom.

E=-RHn2n=1,2,3,......(Forhydrogenatom)RHisRydbergconstant(2.179×10-18J).Eisenergylevel.nisprincipalquantumnumber.

Relation between frequency and wavelength is,

C=λν

C is the speed of light.

is the frequency.

λ is wavelength.

### Explanation of Solution

To calculate: The principal quantum number of higher energy level in Balmer series of hydrogen atom emission spectrum at 397nm .

397 nm = 3.97×10-7m

The wavelength is converted into frequency as follows,

ν=cλ=2.998×108m/s3.97×10-7m=7.551×1014/s

The energy of the transition is calculated as follows,

E==(6.626×10-34J.s)(7.551×1014)=5.0037×10-19J

Emission occurs in balmer series and the change in energy is negative.

E==E4-Ei

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