A physicist is calibrating a spectrometer that uses a diffraction grating to separate light in order of increasing wavelength (λA, λB, and λC). She observes three distinct first-order spectral lines at the following respective angles θm (where m denotes order). θ1 = 12.9°, θ1 = 14.2°, θ1 = 15.0° (a) If the grating has 3,680 grooves per centimeter, what wavelength (in nm) describes each of these spectral lines?

Respuesta :

Answer:

Explanation:

Given

[tex]N=3680 cm^{-1}[/tex]

therefore slit spacing [tex]d=\frac{1}{N}=\frac{1}{3680}=2.717\times 10^{-4}\ cm[/tex]

since [tex]d\sin \theta =n\lambda [/tex]

for [tex]n=1[/tex]

[tex]d\sin \theta =\lambda [/tex]

Now,at [tex]\theta _1=12.9^{\circ},\Rightarrow \lambda _1=6.0657\times 10^{-7}\ m=606.57\ nm[/tex]

at [tex]\theta _2=14.2^{\circ}\Rightarrow \lambda_2=666.5\ nm[/tex]

at [tex]\theta _3=15^{\circ}\Rightarrow \lambda_3=703.21\ nm[/tex]

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