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

Answer:

Explanation:

Given

$N=3680 cm^{-1}$

therefore slit spacing $d=\frac{1}{N}=\frac{1}{3680}=2.717\times 10^{-4}\ cm$

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

for $n=1$

$d\sin \theta =\lambda$

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

at $\theta _2=14.2^{\circ}\Rightarrow \lambda_2=666.5\ nm$

at $\theta _3=15^{\circ}\Rightarrow \lambda_3=703.21\ nm$