   Chapter 30, Problem 53PE

Chapter
Section
Textbook Problem

(a) What is the distance between the slits of a diffraction grating that produces a first-order maximum for the first Balmer line at an angle of 20.0°?(b) At what angle will the fourth line of the Balmer series appear in first order?(c) At what angle will the second-order maximum be for the first line?

(a)

To determine

The distance between the slits of a diffraction grating.

Explanation

Given Data:

Given that slits of a diffraction grating that produces a first order maximum for the first Balmer line at an angle of 20

Formula Used:

The relation between the wavelength and the distance between the slits is given as,

dsinθ=mλ

Where d= Distance between the slits

λ= Wavelength

θ= Angle

m= Order

Wavelength of spectrum lines is given as,

1λ=R(1nf21ni2)

Where λ= Wavelength

R= Rydberg Constant

nf= final energy state of electron

ni= initial energy state of electron

Calculation

Wavelength of first line of Balmer series is calculated as

1λ=R(1nf21ni2)

We have R=1.097×107m1

nf=2

ni=3

Substituting the above values, wavelength is calculated as,

1λ=(1.097×107m1)(122132)

1λ=(1

(b)

To determine

The angle at which the fourth line of Balmer series appear in first order.

(c)

To determine

The angle at which the second order maximum be for the first line.

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