# Three discrete spectral lines occur at angles of 10.1°, 13.7°, and 14.8° in the first-order spectrum of a grating spectrometer. (a) If the grating has 3 660 slits/cm, what are the wavelengths of the light? (b) At what angles are these lines found in the second-order spectrum?

### Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781337553278

Chapter
Section

### Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781337553278
Chapter 37, Problem 18P
Textbook Problem
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## Three discrete spectral lines occur at angles of 10.1°, 13.7°, and 14.8° in the first-order spectrum of a grating spectrometer. (a) If the grating has 3 660 slits/cm, what are the wavelengths of the light? (b) At what angles are these lines found in the second-order spectrum?

(a)

To determine
The wavelengths of the light.

### Explanation of Solution

Given info: Angles of spectral lines are 10.1° , 13.7° and 14.8° , Slits on the grating are 3600slits/cm .

The width of slit can be given as,

d=1N

Here,

N is the number of slits per length.

d is the width of the slit.

Substitute 3600slits/cm for N in the above equation,

d=13600slits/cm=(2.78×104cm)(1m100cm)=2.78×106m

The condition for first order diffraction grating can be given as,

λ=dsinθ (1)

Here,

θ is the angle of spectral line.

λ is the wavelength of light.

For the angle of 10.1° :

Substitute 2.78×106m for d , λ1 for λ and 10.1° for θ in the equation (1),

λ1=(2.78×106m)(sin10.1°)=487.52×109m=487.52nm

Thus, the wavelength of the light is 487.52nm at angle of 10

(b)

To determine
The angles for the lines in the second order spectrum.

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