Chapter 30, Problem 53PE

### College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000

Chapter
Section

### College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000
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 20.0Â°?(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 20âˆ˜

Formula Used:

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

â€ƒâ€ƒdsinÎ¸=mÎ»

Where d= Distance between the slits

â€ƒâ€ƒÎ»= Wavelength

â€ƒâ€ƒÎ¸= Angle

â€ƒâ€ƒm= Order

Wavelength of spectrum lines is given as,

â€ƒâ€ƒ1Î»=R(1nf2âˆ’1ni2)

Where Î»= Wavelength

â€ƒâ€ƒR= Rydberg Constant

â€ƒâ€ƒnf= final energy state of electron

â€ƒâ€ƒni= initial energy state of electron

Calculation

Wavelength of first line of Balmer series is calculated as

â€ƒâ€ƒ1Î»=R(1nf2âˆ’1ni2)

We have R=1.097Ã—107mâˆ’1

â€ƒâ€ƒnf=2

â€ƒâ€ƒni=3

Substituting the above values, wavelength is calculated as,

â€ƒâ€ƒ1Î»=(1.097Ã—107mâˆ’1)(122âˆ’132)

â€ƒâ€ƒ1Î»=(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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