Planck's constant calculated by photoelectric effect laboratory is off

I conducted an experiment today where I had to use a photocathode of unknown material (model: Daedalon Corporation Photoelectric Effect EP-05) and study the photoelectric (PE) effect to make a calculation for Planck's constant $$h$$ as well as the material's work function $$\phi$$. The number I calculated is within the correct order of magnitude, but I think better accuracy is possible through this experiment.

I think my error was due to:

(a) systematic error, or

(b) a fundamental misunderstanding on my part regarding how to define the stopping voltage $$V_s$$ in the experiment which my instructor will not help clarify.

If anyone has a good understanding of these concepts and is willing to help me decipher which it is (and why) I will be very grateful.

This was our PE device:

It is equipped with an ammeter with $$\mathrm{nA}$$ precision and we also connected a voltmeter with $$\mathrm{mV}$$ precision. The whole experiment was performed in the dark with maximum efforts to prevent any stray light from affecting our results so I doubt this is where the error comes from. I turned the voltage knob to maximum (approx $$3.174 \ \mathrm{V}$$) and zeroed the ammeter in the middle to make it easier to read. I first used a mercury lamp with a blue filter. I shined it at the photocathode, the current reading jumped up, then I turned the voltage knob down until the current reached zero again and recorded that value as our stopping voltage $$V_s$$. Is this correct? I asked my professor and he said yes but I thought that we must normalise this value with respect to something.

I repeated this measurement 5 times, recalibrating the zero position each time because of how sensitive the current is. I then repeated the experiment with a green filter and once more with no filter for mercury's UV spectrum line. I then repeated it with a green laser, a blue laser, and a red laser (while still using the appropriate filters).

For each wavelength, I took the mean of the 5 voltage data and then plotted that against $$1/\lambda$$. Since these are photoelectrons, $$1 \ \mathrm{V}$$ should correspond to $$1 \ \mathrm{eV}$$ of energy. So by finding the linear regression, it should be $$V_s=\frac{hc}{\lambda}-\phi$$. Here is my data:

The linear regression is $$y=(705\pm83 \ \mathrm{eV\!\cdot\!nm})x+(-0.55\pm0.18 \ \mathrm{eV})$$. Therefore, by my calculation, $$hc=705\pm83 \ \mathrm{eV\!\cdot\!nm}$$. The accepted value is $$hc=1\,240 \ \mathrm{eV\!\cdot\!nm}$$. This also implies a very low work function of $$0.55\pm0.18 \ \mathrm{eV}$$. According to this paper I found in the Journal of Physics: https://iopscience.iop.org/article/10.1088/1361-648X/aa79bd/meta, the lowest work functions discovered are around $$0.7-0.8 \ \mathrm{eV}$$. Is this the best accuracy I can hope to achieve with this data or have I completely misunderstood/missed something? Any help would be greatly appreciated.

• If you are getting the right order of magnitude for $\hbar$ with only one day's work, you are doing reasonably well. There are tons of difficult to control systematics in an experiment like this, where a very small current is involved.
– Buzz
Commented May 22, 2019 at 1:35
• Determination of Planck’s Constant Using the Photoelectric Effec Commented Oct 25, 2021 at 8:07