Alight with a second-order dark band forms a diffraction angle of 20.0°. the diffraction grating has 200.0 lines per mm. the wavelength of the light, to the nearest whole number, is nm.

the correct answer is 684 nm

684 nm

Explanation:

For n order dark band for diffraction pattern formed by diffraction grating:

d sin θ = (n + 0.5) λ

where, d is the distance between the slits

d = 1/N where N is the number of slits per unit length

θ is angle of diffraction. (θ =20°)

n is integral number ( n =2 for second order)

λ is the wavelength.

d = 1/200 mm = 0.005 mm

⇒λ = (0.005 mm × sin 20°) ÷ (2+0.5) = 684 nm

Thus, the wavelength of light is 684 nm.

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