   Chapter 30, Problem 69PE

Chapter
Section
Textbook Problem

Unreasonable ResultsA student in a physics laboratory observes a hydrogen spectrum with a diffraction grating for the purpose of measuring the wavelengths of the emitted radiation. In the spectrum, she observes a yellow line and finds its wavelength to be 589 nm. (a) Assuming this is part of the Balmer series, determine n i , the principal quantum number of the initial state. (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

To determine

(a)

A student in a physics laboratory observes a hydrogen spectrum with a diffraction grating for the purpose of measuring the wavelengths of the emitted radiations. In the spectrum, she observes a yellow line and find its wavelength to be589nm . Assume this to be part of Balmer series, determineni , principal quantum number of the initial state.

Explanation

Given Data:

Given that yellow line is observed and its wavelength to be589nm.

Formula Used:

Wavelength can be calculated as follows

1λ=R(1nf21ni2)

WhereR= Rydberg Constant

nf= Final energy state of electron

ni= Initial energy state of electron

Calculation:

We know that wavelength is calculated as

1λ=R(1nf21ni2)

Rearrange the above formula

1ni2=1nf21λR

ni=λRnf2λRnf2

We haveR=1

To determine

(b)

To determine

(c)

Which assumptions are unreasonable or inconsistent?

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