Understanding a particular spectrum is important in many areas of science, inclu

Question

Understanding a particular spectrum is important in many areas of science, including physics and chemistry, where it can be used to identify a gas, for instance. To create a spectrum, light is generally sent through a diffraction grating, splitting the light into the various wavelengths that make it up. (a) The first step in the process is to calibrate the grating, so we know the grating spacing (the distance between the openings in the grating). Sodium has two yellow lines that are very close together in wavelength at 590 nm. When light from a sodium source is passed through a particular diffraction grating, the two yellow lines overlap, looking like one line at an angle of 31.1 degrees in the first-order spectrum. What is the ratingspacing? nm (b) The hydrogen atom is the simplest atom there is, consisting of one electron and one proton, and it has thus been well studied. When hydrogen gas is excited by means of a high voltage, three of the prominent lines in the spectrum are found at wavelengths of 656.3 nm, 486.1 nm, and 434.1 nm. When the light is passed through the diffraction grating we calibrated with sodium, at what angles will these two lines appear in the first-order spectrum? Scientists observing these lines can be confident that the source of the light contains hydrogen. 656.3 nm line 434.1 nm line

Explanation / Answer

use the formula from Diffraction grating as

d sin theta = mL

here L = wavelength = 590nm

theta = angle = 31.1 deg

d sin (31.1) = 1 * 590 *10^-9

d = (590 *10^-9)/(sin(31.1)

d =   1142.23 nm is the grating spcaing
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part B:

Now again,

d sin theta = 1 * L

for wavelength L = 656.3 nm

sintheta = 1* 656.3*10^-9/(1142.23*109^-9)

sin theta = 0.574

theta = 35 deg

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for L = 434.1 nm

sin theta = 1* 434.1*10^-9/(1142.23*109^-9)

sin theta = 0.38

theta = 22.33 deg

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