I need step by step caluclations with an explanation if needed. 1. A grating has

Question

I need step by step caluclations with an explanation if needed.

1. A grating has 6250lines/cm. What is the grating spacing in nm?

2. For the above grating calculate the angle of a second order orange line of wavelength 600nm?

3. Convert the spectroscope reading 228angle 16' ('minutes) to decimal degree reading?

4. In an experiemnt you measure a first order red line for hydrogen at an angle difference of deltaangle=22.78. The diffraction grating you are using has 5900 lines per cm.

a. What is the wavelength of this light?

b. What is the value of Rydberg's constant for this measurement?

Explanation / Answer

1)

Here m

number of lines = 6250 lines/cm

spacing of grating = 1/6250 cm

spacing of grating = 1.6 *10^-4 cm

spacing of grating = 0.0016 mm

the spacing of grating is 0.0016 mm

2)

for the second order orange line ,

as d * sin(theta) = m * wavelength

1.6 *10^-4 * 10^-2 * sin(theta) = 2 * 600 *10^-9

solving for theta

theta = 48.6 degree

the angle theta is 48.6 degree

3)

angle = 228 degree 16 minutes

angle = 228 + 16/60 degree

angle = 228 + 0.267

angle = 228.267 degree

the angle is 228.267 degree

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