Light emitted by element X passes through a diffraction grating that has 1200 slits/mm. The interference pattern is observed on a screen 75.0 cm behind the grating. First-order maxima are observed at distances of 56.2 cm, 65.9 cm, and 93.5 cm from the central maximum. What are the wavelengths of light emitted by element X?

Question

Physics

Davis Branch

9 January, 19:19

Light emitted by element X passes through a diffraction grating that has 1200 slits/mm. The interference pattern is observed on a screen 75.0 cm behind the grating. First-order maxima are observed at distances of 56.2 cm, 65.9 cm, and 93.5 cm from the central maximum. What are the wavelengths of light emitted by element X?

+5

Answers (1)

Know the Answer?

Maxwell Anderson · Answer 1

Width of slit = 10⁻³ / 1200

d = 8.3 x 10⁻⁷ m

First order maxima will be observed at

x = λD/d

D = 75 cm = 75 x 10⁻² m

56.2 x 10⁻² = λ₁D/d

= λ₁ x 75 x 10⁻² / 8.3 x 10⁻⁷

λ₁ = 56.2 x 8.3 x 10⁻⁷ / 75

= 6.219 x 10⁻⁷ m

= 6219 A

Similarly

λ₂ = 65.9 x 8.3 x 10⁻⁷ / 75

= 7293 A

λ₃ = 93.5 x 8.3 x 10⁻⁷ / 75

= 10347 A