Spectra Lab

Purpose: 
To observe the various color spectra through small slits: to view what a white light is composed of , and to measure the spectra of hydrogen gas. The spectra will be observed by calculating its wavelength obtained by measuring the distance/ separation of each spectra.

Materials: 
White light source
Meter sticks
Diffraction lens
Marker
Various gas (light source)

λ/d = D/(L^2 + D^2)^0.5

or

λ = D * d / (L^2 + D^2)^0.5

λ is the wavelength of each spectrum

D is the distance from light source to observer

d is the distance between the slits

(L^2 + D^2)^0.5 is the distance from observer to the spectrum (forms a triangle)

I. Measuring spectra of white light

White light consists of all colors, as shown above^. The first part of the experiment measures the location of each color to determine the wavelength of each color.

Length is 1.00 m + 0.05 

d is 2*10^-6 m

The colors, in order, are as follows:

	Violet	Indigo	Blue	Green	Yellow	Red
D (m)	0.199	0.223	0.251	0.289	0.303	0.411
λ	3.90346E-07	4.35308E-07	4.86897E-07	5.5528E-07	5.7996E-07	7.6029E-07
λ actual	0.0000004	0.000000445	0.000000475	0.00000051	0.00000059	0.00000065

Calibration graph (y axis = actual value, x axis = observed values)

λ adjusted

3.6766E-07

3.9849E-07

4.33865E-07

4.80753E-07

4.9768E-07

6.21331E-07

The adjusted λ ranges from 370 to 620 nm; this is because the graph itself is not linear. R squared is 0.93, which is far from 1. It is expected to see adjusted λ values that is off from the actual values.

wavelength in nm

390.345995

435.3076116

486.8967555

555.276344

579.9616666

760.2899278

Uncertainty in nm

4.82700251

4.846194215

5.948377766

22.638172

5.019166705

55.14496391

Wavelength with uncertainties: 

λ1 = 390 + 4.8 nm

λ2 = 435 + 4.8 nm

λ3 = 487 + 5.9 nm

λ4 = 555 + 23 nm

λ5 = 580 + 5.0 nm

λ6 = 760 + 55 nm

II. Measuring spectra of unknown gas and hydrogen

The second part of the experiment, an unknown gas and a hydrogen light sources were used. Different light spectra were observed.

(The unknown that was assigned was unknown #3, which was He)

D and wavelength are as follows:

He spectrum observed values:

	Violet	Blue	Green	Yellow	Red
D (m)	0.216	0.242	0.276	0.324	0.373
λ (nm)	394.1	442.7	505.1	572.9	674.1

Actual values:

Actual
λ (nm)	438.8	447.1	501.6	587.6	667.8

Calibration: y = 0.877x + 74.6 

Uncertainty

22.35

2.2

1.75

7.35

3.15

λ1 = 394.1 + 22.35 nm

λ2 = 442.7 + 2.2 nm

λ3 = 505.1 + 1.75 nm

λ4 = 674.1 + 3.15 nm

Hydrogen Spectrum

Observed values:

	Violet	Green	Yellow	Red
D (m)	0.221	0.252	0.282	0.308
λ (m)	4.31586E-07	4.89E-07	5.43E-07	5.89E-07
λ (nm)	432	489	543	589

Actual
λ (nm)	435	520	565	625

Calibration: y = 1.17x - 65.7 

Uncertainty

1.5

15.5

11

18

λ1 = 432 + 1.5 nm

λ2 = 489 + 15.5 nm

λ3 =543 + 11 nm

λ4 = 625 + 18 nm

Conclusion:

The spectra lab measures the different emitted light spectra when light travels through the diffraction gratings (small slits), causing the object (light source) to emit emissions of different wavelengths. The first experiment measures normal white light source. It appears that white light source emits all the visible color. The second and third experiment measures hydrogen and unknown (helium) gas light source. Being different from white light source, the spectra appears to be single lines. The wavelength of each corresponding lines could be measured by finding the distance (D) from the light source. Most of the measurements have uncertainty ranging from 5-20 nm, with few spectra exhibiting uncertainty of >20 nm, and one >50 nm.