Question

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?

Answer 1

Step-by-step explanation:

Given

`N=3680 cm^(-1)`

therefore slit spacing
`d=(1)/(N)=(1)/(3680)=2.717* 10^(-4)\ cm`

since
`d\sin \theta =n\lambda`

for
`n=1`

`d\sin \theta =\lambda`

Now,at
`\theta _1=12.9^(\circ),\Rightarrow \lambda _1=6.0657* 10^(-7)\ m=606.57\ nm`

at
`\theta _2=14.2^(\circ)\Rightarrow \lambda_2=666.5\ nm`

at
`\theta _3=15^(\circ)\Rightarrow \lambda_3=703.21\ nm`