Physics307L F09:People/Mondragon/Notebook/071017

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FIRSTWEEK

data for planck's constant

SETTLE VOLTAGE FOR YELLOW ORANGE:=652mV

stop=612mv

1.28s @100%

1.20s @80%

1.72s @60%

2.04s @40%

4.92s @ 20%

SETTLE VOLTAGE FOR GREEN:=800mV

STOP=712mV

1.40s @100%

2.10s @80%

2.50s @ 60%

4.90s @40%

12.0s @20%


SETTLE VOLTAGE FOR BLUE;=1.37V

STOP=1.23V

1.20s @ 100%

2.00s @ 80%

2.00s @60%

2.80s @ 40%

7.40s @ 20%

Settle voltage for purple=1.50V

stop=1.34V

1.28s @100%

1.40s @80%

1.56s @60%

1.92s @40%

5.76s @20%

settle for UV=1.80V

stop=1.62V

6.2s @100%

6.4s @80%

9.7+/-2.0s @60%

17.4s @40%

81s @20%


Methodology

Following instructions in Dr. Gold's lab manual, I made sure the equipment was set up correctly to perform the experiment. First, one should get the light from the lamp as focused as possible by adjusting the diffraction grating/lens. Next, one should make sure light from the lamp reaches the photocathode of the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \tfrac{h}{e}} apparatus. How to do this is described in the manual. (perhaps I should upload the manual in case www-hep.unm.edu goes down again) following that, one should test the batteries of the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \tfrac{h}{e}} apparatus. I suppose the minimum ratings for the batteries are listed were the apparatus's test points are, so they are +6V and -6V. Measure using a multimeter from the apparatus's ground to each of the battery test points. I measured +8.70V and -8.69V, so the batteries were fine.

All of the outputs of the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \tfrac{h}{e}} device are made for banana clips. The lab manual suggests using a stopwatch and a multimeter to measure the rise time. But, since we wanted to use an oscilloscope to measure rise time more accurately, we has to use a banana to BNC connector. It seems like the connector, and maybe the BNC cable and the BNC input of the oscilloscope, caused some weirdness in the voltage output.

If the quantum description of light was correct, then for a certain light frequency Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle f} the voltage output from the apparatus would rise exponentially and settle to a stopping voltage Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle V_o(f)} like the voltage across a capacitor would rise as the capacitor was charging. When we where using just the multimeter this definitely seemed like the case. But, when we had the voltage output going to the oscilloscope, the voltage often exhibited a very sharp rise followed by either an exponential decay to some voltage Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle V > V_o(f)} or a sharp drop followed by an exponential rise and settle to Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle V_o(f)} .

Theory

The Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \tfrac{h}{e}} apparatus is basically a capacitor. One plate is a photocathode. Light shining on the photocathode gives electrons the energy necessary to escape the surface of the cathode and to possibly cross the gap to the anode. As charge builds up on the anode, the voltage across the capacitor will increase, as will the energy necessary for electrons to cross the gap.

Just for future reference, I doubt I'll be using it though Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle q=C*V} , where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle q} is the absolute value of charge on one plate of the capacitor, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle V} is the absolute value of the voltage across the capacitor, and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle C} is the capacitance of the capacitor.

The energy needed by an electron to escape the photocathode's surface is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle W_0} . Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle W_0} is a property of the photocathode. After light imparts its energy onto en electron, part of the energy will be used to escape the photocathode (if Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle E_{light} \ge W_0} ), and the rest manifests itself as the kinetic energy of the now free electron, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle KE_{max}} . Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle E_{light} = W_0 + KE_{max}}

Because of the voltage across the capacitor, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle KE_{max}} must be more than a certain potential energy Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle PE_{gap}} created by the voltage difference. The potential energy that needs to be overcome is proportional to the voltage difference. When Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle PE_{gap} \ge KE_{max}} , electrons can no longer reach the anode so the voltage no longer rises. This final voltage is called Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle V_{stop}} . Because of the way capacitors charge, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle V_{stop}} is never actually reached in a finite amount of time. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle V_{stop}} is proportional to Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle KE_{max}} .

Electrons can only make it to the anode if Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle KE_{max} < PE_{gap}= e\,V} . Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle KE_{max}} should, in this experiment, stay the same thoughout a test, but Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle PE_{gap}} changes as Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle V} changes. When Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle V_{stop}} is reached, it is because Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle KE_{max} = PE_{gap}= e\,V_{stop}}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \begin{align} E_{light} &= W_0 + KE_{max}\\ E_{light} &= W_0 + e\,V_{stop}\\ \frac{E_{light}}{e} &= \frac{W_0}{e} + V_{stop}\\ \end{align} }

According to the particle theory of light, the energy imparted by light is proportional to the frequency of the light, the constant of proportionality being Plank's constant. According to the wave theory of light, the energy imparted by light is proportional to the square root of the intensity of the light. The data shows that the stopping voltage doesn't change when the light intensity changes, but it does when the light frequency changes. So

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \begin{align} E_{light} &= W_0 + KE_{max}\\ E_{light} &= W_0 + e\,V_{stop}\\ \frac{E_{light}}{e} &= \frac{W_0}{e} + V_{stop} &= \frac{h\nu}{e}\\ V_{stop} &= \frac{h\nu}{e} - \frac{W_0}{e}\\ \end{align} }

ν is the frequency of the light falling on the photocathode and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle h} is Plank's constant.

table!!

color frequency settle voltage
Yellow Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle 5.18672*10^{-14}} Hz 652 mV
Green Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle 5.48996*10^{-14}} Hz 800 mV
Blue Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle 6.87858*10^{-14}} Hz 1.37 V
Violet Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle 7.40858*10^{-14}} Hz 1.50 V
Ultraviolet Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle 8.20264*10^{-14}} Hz 1.80 V

fit is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle V_{stop}=\tfrac{h}{e}*\nu+\tfrac{W_0}{e} \, \, , \,\tfrac{h}{e}=0.377989*10^{-14}\pm 0.014521*10^{-14} \,V*s \,\tfrac{W_0}{e}=-1.282910 \pm 0.097743\,V} FreqandVoltage.png

so, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle h=3.77989*10^{-15}\pm 0.14521*10^{-15} \,eV*s} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle W_0=1.282910 \pm 0.097743\,eV} . The accepted value of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle h} , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle h =\,\,\, 6.626\ 068\ 96(33) \times 10^{-34}\ \mbox{J}\cdot\mbox{s} \,\,\, = \,\,\, 4.135\ 667\ 33(10) \times10^{-15}\ \mbox{eV}\cdot\mbox{s} } is within three standard deviations of my calculated value. Looks like a systematic error.