Different isotopes of the same element emit light with slightly different wavelengths. The wavelength in the emission spectrum of the hydrogen atom is 656.45 nm; for deuterium, the corresponding wavelength is 656.27 nm. (a) What is the minimum number of slits required to separate these two wavelengths in the second order? (b) If the grating has 500.00 slits / mm, find the angles and the angle of separation of these two wavelengths in the second order.

Marcus Bass 2022-09-26 Answered
Different isotopes of the same element emit light with slightly different wavelengths. The wavelength in the emission spectrum of the hydrogen atom is 656.45 nm; for deuterium, the corresponding wavelength is 656.27 nm. (a) What is the minimum number of slits required to separate these two wavelengths in the second order? (b) If the grating has 500.00 slits / mm, find the angles and the angle of separation of these two wavelengths in the second order.
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Answers (1)

Nancy Ewing
Answered 2022-09-27 Author has 7 answers
Given,Hydrogen wavelength, λ H = 656.45   n m = 656.45 × 10 9   m, deuterium wavelength, λ H = 656.27   n m = 656.427 × 10 9   m.
The number of slits is given by,
N = λ m Δ λ = 656.45 × 10 9 m 2 × ( 656.45 × 10 9 m 656.27 × 10 9 m ) = 656.45 × 10 9   m 2 × 0.18 × 10 9   m = 1823.47 = 1823
The angle is given by,
θ = sin 1 ( m λ d ) = sin 1 ( 2 × 656.45 × 10 9 m × 500000   m 1 ) = 41.0297 0
And,
θ = sin 1 ( m λ d ) = sin 1 ( 2 × 656.27 × 10 9 m × 500000   m 1 ) = 41.0160 0
Hence, the angle between is,
Δ θ = θ θ 1 = 41.0297 41.0160 = 0.0137 0
Hence, the slits number is 1823, angles are 41.0297 0 and 41.0160 0 . The angle difference is 0.0137 0
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