The purpose: We are going to measure the wavelength of a white light source, and we find the name of two unknown gases (mercury gas and hydrogen gas), by measuring their wavelength.
First of all, we put two meters sticks that one is 1 meter and the another is 2 meters perpendicular to other each, and we put a white light bulb at the intersection point of two meter sticks.
We use diffraction grating to see the diffraction pattern of the white pattern, and we draw the pattern from red color to violet color.
We measure the reading of 1 meter of both end of different color fringes, we subtract every value of end so we have the width of the fringe.
We use the equation λ= s*D/(d^2+D^2)^1/2, where s is 1.75975698*10^-6m.
| Color | D (cm) | λ (m) |
| Violet | 45.1 | 3.87*10^-7 |
| Blue | 51.3 | 4.37*10^-7 |
| Green | 59.9 | 5.05*10^-7 |
| Yellow | 66.5 | 5.55*10^-7 |
| Red | 78.1 | 6.40*10^-7 |
We offset the wavelength measured to match the actual wavelength by adding 30*10-9.
| λ measured (m) | λ after offset (nm) |
| 3.87*10^-7 | 417 |
| 4.37*10^-7 | 467 |
| 5.05*10^-7 | 535 |
| 5.55*10^-7 | 585 |
| 6.40*10^-7 | 670 |
After that, we measure the two gases, and we find out the gas by measuring their wavelength.
(Mercury gas)
We replace white source with mercury gas (we do not know yet).
We use the same equation to find the wavelength.
There are not blue and red fringes.
| Color | D(m) | λ (m) |
| Violet | 0.475 | 4.07E-07 |
| Green | 0.605 | 5.10E-07 |
| Yellow | 0.655 | 5.48E-07 |
We look at the spectrum to find the actual wavelength, and we compare the measured and actual wavelength.
| λ (m) | λ Acutal(m) |
| 4.07E-07 | 4.30E-07 |
| 5.10E-07 | 5.48E-07 |
| 5.48E-07 | 5.77E-07 |
We check that we measure the wavelength correct by multiple every measured wavelength by 1.0642, which is closed to the actual wavelength.
(Hydrogen)
We replace mercury gas with hydrogen gas(we do not know yet).
We use the same equation to find the wavelength.
There are not green and yellow fringes.
We also offset the measured wavelength by multiple 1.06 which is the ratio of measured wavelength and actual wavelength found in mercury gas part, and we compare the measured wavelength and actual wavelength.| Color | D(m) | λ (m) | λ offset (m) | λ Acutal(m) |
| Violet | 0.482 | 4.12E-07 | 4.37E-07 | 4.34E-07 |
| Blue | 0.537 | 4.56E-07 | 4.83E-07 | 4.86E-07 |
| Red | 0.745 | 6.14E-07 | 6.51E-07 | 6.56E-07 |
The offset wavelength is closed to actual wavelength as the slope is 1.031 closed to 1.
We find the wavelength of the violet color (4.38E-7) that is closed to the energy for an electron moves from 5th to 2nd level (4.34E-7) in hydrogen atom.
We find the wavelength of the blue color (4.85E-7) that is closed to the energy for an electron moves from 4th to 2nd level (4.86E-7) in hydrogen atom.
We find the wavelength of the red color (6.53E-7) that is closed to the energy for an electron moves from 3th to 2nd level (6.56E-7) in hydrogen atom.
So we check that we measure the wavelength correctly.
As a result, we successfully measure the wavelength of a white light source, and we find the name of two unknown gases which are mercury gas and hydrogen gas by measuring their wavelength.
