Particle in a Box

We looked at problems/simulations on the Pearson physics website for section 20.2 LINKAGE

Answers to the questions:
1. λ=2*L
2. λ=h/p = h/(2L)
3. E=p^2/(2m) = h^2/(8m*L)
4. it will decrease
5. ground state ->0 & spacing goes to 0
6. Ground state energy and spacing is 0
7. the center of the box
8. It doesn't, it depends on L
9. Yes, probability of detection stays highest at the center
10. As n gets larger, regions of probability blur together.

Planck's constant from an LED

In this lab, we can use the principles on which an led operates to experimentally determine planck's constant.
We know the following relationships:
λ=h/mv
E=hf=hc/λ

We used 4 different color LEDs: Red, yellow, green, and blue. We ran the experiment the same exact way as the hydrogen and color spectra lab.

Color	Distance D (meters)	Voltage (Volts)	Wavelength (nm)
Yellow	0.67	1.88	592.43
Green	0.59	2.52	529.04
Red	0.735	1.82	641.93
Blue	0.525	2.64	475.63

Using the fact that E=hc/λ=q*V, we get that h = q*V*λ/c

Color	Wavelength (nm)	Voltage (Volts)	h
Yellow	592.43	1.88	5.94E-34
Green	529.04	2.52	7.11E-34
Red	641.93	1.82	6.23E-34
Blue	475.63	2.64	6.70E-34

From these results, only blue seems to give a value that was within scientifically acceptable bounds of the theoretical value at 1.12% error. Red also came in at a relatively low error of 5.98%. Both Yellow and Green had relatively high error. Coincidentally, their spectra also contained various colors which made it hard to pinpoint the maxima that corresponded to the color of the LED itself. This is likely due to the fact that the green LED had impurities and was contained additional wavelengths. The particular shade of yellow also had an orange tinge to it. Overall, it appears that the colors on the ends of the visible spectrum were much easier to identify.

Color and hydrogen spectrum

This lab uses a diffraction grating to analyze wavelengths of light from a specific light source.
Our setup was as shown.

We placed a light source at the origin of the 2 rulers, placed a diffraction grating at a distance from the bulb, and looked through it and measured the range of wavelengths.We use the following formula:

where λ is the wavelength, d is the slit spacing on the diffraction grating, D is the observed horizontal distance from the light source to the band of light, L is the distance from the diffraction grating to the light.
 We took readings at 2 distances to minimize error.

L (m)	Red(D)	Violet (D)
1.5	0.65	0.3
1.8	0.745	0.35

We were then given a gas discharge tube, and our job was to determine what type of gas was in the tube based on the spectral lines we observe.

We compared the spectral bands with a chart of different gasses' spectral lines, and they corresponded almost perfectly with mercury.

color	D (m)	Measured λ	Theoretical λ
Red	0.75	690	690
Yellow	0.61	589	580
Green	0.54	535	545
Violet	0.42	439	435

We plot the measured values against the theoretical values to get a correction value of 75 nm.
We were then given a hydrogen discharge tube, and measured the spectral lines of hydrogen.

D (m) λ (Measured) (nm) λ (Calculated) (nm) λ (Theoretical) (nm) Red (D) 0.7 655 654 656 Blue (D) 0.49 495 495 486 Violet (D) 0.43 447 446 434

The different spectral lines indicate the different energy levels that the hydrogen can transition between. For each of these transitions, the hydrogen emits a photon corresponding to a specific wavelength. This method can be used to analyze an unknown gas and determine it's composition based on the energy levels.