In the cchemistry lab we conducted an experiment called atomic spectroscopy.

We had to find the color, energy, wavelength, and 1/lamda for Hydrogen, neon, and mercury.

For hydrogen:
red 1.90ev 650nm 1.54e^-3
red 2.02ev 610nm 1.64e^-3
green 2.30ev 545nm 1.83e^-3

for neon:
green 2.30ev 550nm 1.82e^-3
red 2.05ev 610nm 1.64e^-3
red 1.80ev 690 1.45e^-3
yellow 2.12 580 1.72e^-3
blue 2.65 470 2.13e^-3

for mercury:
green 2.30ev 548 1.823^-3
red 2.05 590 1.69e^-3
violet 2.85 440 2.27e^-3
blue 2.55 470 2.13e^-3
yellow 2.15 570 1.75e^-3

for the first question we had to derive the equation that would allow us to find Planck's constant from your graph using the formulas
c= lamda X v and E=hv

The teacher said that the equation is h=slope / c

The next question says to show the calculations of Planck's constant, including the unit conversions, for mercury, neon, and hydrogen using the equation created above.

I am not sure how to do this. I do not know where to start.

We had to create graphs for neon and hydrogen on the computer so would i use the slope from there?

What were your axes? What did you plot on the x axis and what on the y axis?

The slope is delta y/delta x.

on the x axis was 1/wavelength (nm-1) and the y axis was energy(ev). The line for both graphs of neon and hydrogen was positive. So would I pick two points on the graph to find the slope and then do h=slope/c?

To calculate Planck's constant for each element (mercury, neon, and hydrogen), you need to use the equation you derived: h = slope / c.

1. Start by calculating the slope of the graph for each element. The slope represents the change in energy (y-axis) per change in wavelength (x-axis) and can be determined by selecting two points on the graph and calculating the rise over run.

For example, for hydrogen:
- Select two points on the graph, let's say (650 nm, 1.90 eV) and (610 nm, 2.02 eV).
- Calculate the change in energy: 2.02 eV - 1.90 eV = 0.12 eV.
- Calculate the change in wavelength: 610 nm - 650 nm = -40 nm. Note: The negative sign indicates a decrease in wavelength.
- Calculate the slope: change in energy / change in wavelength = 0.12 eV / -40 nm.

Repeat this process to calculate the slope for neon and mercury using the respective data points.

2. Convert the slope to the proper units. The slope you obtained in the previous step likely has units of eV/nm. To convert it to the appropriate unit for Planck's constant, which is joule-seconds (J·s), you need to convert eV to joules and nm to meters.

- The conversion factor for eV to joules is 1 eV = 1.602 x 10^-19 J.
- The conversion factor for nm to meters is 1 nm = 1 x 10^-9 m.

Multiply the slope by both conversion factors to obtain the slope in J·s/m.

3. Calculate Planck's constant by dividing the slope by the speed of light (c). The speed of light is a constant value equal to approximately 3.00 x 10^8 m/s.

For example, for hydrogen:
- Divide the slope (in J·s/m) by the speed of light (in m/s) to give you Planck's constant. h = slope / c.

Repeat this calculation for neon and mercury using their respective slopes and the speed of light.

4. Make sure to include the appropriate units in your final answer.

So, to summarize:
- Calculate the slope of the graph for each element (change in energy / change in wavelength).
- Convert the slope to J·s/m by multiplying by appropriate conversion factors.
- Divide the slope by the speed of light to obtain Planck's constant for each element.
- Make sure to include units in your final answer.

Note: If you created graphs on the computer, you can use the slope obtained from those graphs as long as they represent the change in energy per change in wavelength.