A diffraction grating is placed 1.00 m from a viewing screen. Light from a hydrogen lamp goes through the grating. A hydrogen spectral line

Question

A diffraction grating is placed 1.00 m from a viewing screen. Light from a hydrogen lamp goes through the grating. A hydrogen spectral line with a wavelength of 656 nm is seen 60.0 cm to one side of the center. Then, the hydrogen lamp is replaced with an unknown lamp. A spectral line is seen on the screen 36.4 cm away from the center. What is the wavelength of this spectral line

in progress 0
Dulcie 6 months 2021-08-27T20:38:43+00:00 1 Answers 3 views 0

Answers ( )

    0
    2021-08-27T20:39:54+00:00

    Answer:

    λ = 396.7 nm

    Explanation:

    For this exercise we use the diffraction ratio of a grating

               d sin θ = m λ

    in general the networks works in the first order m = 1

    we can use trigonometry, remembering that in diffraction experiments the angles are small

               tan θ = y / L

               tan θ = \frac{sin \theta}{cos \theta} = sin θ

               sin θ = y / L

    we substitute

              d \  \frac{y}{L} = m λ

    with the initial data we look for the distance between the lines

               d = \frac{m \lambda \ L}{y}

               d = 1 656 10⁻⁹ 1.00 / 0.600

                d = 1.09 10⁻⁶ m

    for the unknown lamp we look for the wavelength

               λ = d y / L m

               λ = 1.09 10⁻⁶ 0.364 / 1.00 1

               λ = 3.9676 10⁻⁷ m

               λ = 3.967 10⁻⁷ m

             

    we reduce nm

               λ = 396.7 nm

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )