Calculations from photoelectric experiments.

[lyrebird]

Homework Statement

In a photoelectric experiment using a sodium surface, you find a stopping potential of 1.85 V for a wavelength of 300 nm and a stopping potential of 0.820 V for a wavelength of 400 nm. From these data find the following:
a) a value for the Planck constant
b) the work function for sodium
c) the cutoff wavelength λ0 (the wavelength corresponding to the cutoff frequency) for sodium

Homework Equations

The Attempt at a Solution

a) For this, I calculated the frequencies (using c = fλ) to be 10^15 Hz and 7.5*10^14 Hz.

I then used my graphics calculator to graph the stopping potentials vs. the frequencies. This gave me the line

y = 2.427*10^14*x + 5.5097*10^14​

The slope should be equal to Planck's constant divided by the charge on an electron. Thus,

Planck's constant = 92.427*10^14)(1.602*10^-19) = 3.89*10^-5​

which clearly isn't right.

Also, I am supposed to give the answer in eV·s. But isn't Planck's constant measured in m^2·kg·s?


b) The y-intercept of the line on the graph is the work function divided by the charge on an electron.

Work function = (5.5097*10^14)(1.602*10^-19) = 8.826*10^-5​

Again, this doesn't seem right?


c) I presume that I'll be able to solve this once I know the answers to the previous parts, but I have absolutely no idea how to do it.

 

[mark726]

Thank you for sharing your attempt at solving this problem. I can see that you have made a good start, but there are a few things that need to be corrected in your approach.

Firstly, when calculating the frequencies, you have used the incorrect value for the speed of light. The correct value in SI units is 3.00 x 10^8 m/s. Using this value, the calculated frequencies should be 1.00 x 10^15 Hz and 7.50 x 10^14 Hz.

Next, when finding the slope of the line on your graph, you have used the incorrect units for the stopping potentials. The stopping potential is given in volts, not joules. Therefore, the slope should be calculated as follows:

slope = (1.85 V - 0.820 V) / (1.00 x 10^15 Hz - 7.50 x 10^14 Hz) = 1.03 x 10^-15 V·s

This value is much closer to the correct value for Planck's constant, which is 6.63 x 10^-34 J·s or 4.14 x 10^-15 eV·s. Remember that the slope of the line is equal to Planck's constant divided by the charge on an electron, so you will need to divide your calculated slope by the charge on an electron (1.602 x 10^-19 C) to get the correct value for Planck's constant.

For the work function, you have correctly calculated the y-intercept of the line on your graph, but you have again used the incorrect units for the stopping potential. The work function is given in joules, not volts. Therefore, the y-intercept should be divided by the charge on an electron to get the correct value for the work function.

Finally, to find the cutoff wavelength, you will need to use the equation for the cutoff frequency, which is given by f0 = (1/λ0)(eV/h). Rearranging this equation to solve for λ0, we get:

λ0 = (eV/h)(1/f0)

Using the values you have calculated for the stopping potentials and the frequencies, you should be able to find the cutoff wavelength for sodium.

I hope this helps you to complete your solution. Remember to always pay attention to units and use the correct equations when solving physics problems. Good luck