User:David K. O'Hara/Notebook/physics 307 lab/planck's constant (h/e

Introduction

In 1901 Planck published his law of radiation. He stated that an oscillator or any similar system, has a discrete set of possible energy levels. He also stated that the emission and absorption of radiation is associated with transitions between these energy levels. The energy lost or gained by an oscillator is emitted or absorbed as a quantum of radiant energy which can be expressed as E=hν. Where h is a fundamental constant of nature, which later became known as Planck's Constant. In this experiment we will find the value of h and compare how close it is to the accepted value of this constant.

Equipment

Mercury Vapor Light Source and Light Block(Model OS-9286)

Light Aperture (Model AP-9369)

Coupling Bar (Model AP-9369)

Digital Voltmeter (Model 37XR-A)and/or (model FLUKE 111)

Stopwatch

Two 9 Volt Batteries

h/e Apparatus (Model AP-9369)

3 Filters

• Relative Transmission
• Yellow Line
• Green Line

Safety

As with all electrical systems care should be taken to insure all cables are in good shape with no worn patches. Mercury lamp will be very hot after continuous running, so care should be taken when manipulating the lamp box. As it is a mercury lamp, care should be taken when handling to make certain the lamp will not be damaged in any way.

Procedure

Experiment was conducted using the procedure found in Dr. Gold's Lab Manual [|lab manual]

• 1. Begin by allowing mercury lamp to heat up for about 5 minutes.
  
• 2. While lamp is heating up, check the 9 volt batteries in the h/e apparatus to verify they are both putting out at least 8 volts each to insure the h/e apparatus will function properly. (measured values were 8.81 volts and 8.80 volts).
  
• 3. Connected the DVM to the h/e apparatus output.
• 4. Aligned the aperture and light source so that the diffraction band was pretty well centered on the lens of the h/e apparatus.
  
• 5. Focused the diffracting lens so the light pattern had very sharp resolution right at the lens of the h/e apparatus.
  
• 6. Took the DVM reading as each maxima was aligned with the h/e apparatus window.

Data

Experiment 1
In the first experiment we used the intensity filter to allow different amounts of light through to the h/e apparatus window. Once the different colors (wavelengths) were lined up with the window, the zero button on the h/e app. was hit to discharge any accumulated charge. We then measured the stopping potential, and we timed how long it took the voltmeter reading to return to that same stopping potential. We used only the first maxima of the diffraction pattern for these readings.

Experiment 2
In the second experiment I took measurements for the stopping potential for each of the five wavelengths of light listed in the lab manual at the first and second maxima. this data was then used to calculate a value for h using the relationship E=hν=KE_max+W₀.

Wavelength and frequency of diffraction lines

• ultraviolet 8.20264e14 hz 365.483 nm
• violet 7.40858e14 hz 404.656 nm
• blue 6.87858e14 hz 435.835 nm
• green 5.48996e14 hz 546.074 nm
• yellow 5.18672e14 hz 578.000 nm

i couldn't format a table using openwetware that I liked so all the data + analysis is in this excel sheet. File:Planck.xlsx

During measurement of the green second maxima the first voltage I measured was 1.207 volts when it should have been in the .800 volt range. Investigation found that the green filter which according to the lab manual will prevent uv light from overlapping maxima from interfering with current readings, was not sufficient to the task of blocking extraneous uv light. Considering the data I got had my value for Planck's constant end up high, I suspect that none of the filters are "perfect" blockers of uv light.

Analysis

The basis for this experiment to find a value of Planck's constant hinges on the following mathematical course: The total energy for electrons leaving the cathode in this experiment is given by:

• E=hν=KE_max+W₀

The Kinetic energy of the electrons is:

• KE = 1/2 m_ev²

The stopping potential is where the potential barrier is equal to the kinetic energy of the electron:

• eV_s=KE_max

Which leads to:

• E=hν=eV_s+W₀

• eV_s=hν-W₀

where e=1.602E-19

• V_s=(hν-W₀)/e

So, after graphing frequency vs stopping potential, multiplying the slope by e I obtained a value for h. Then multiplying the y-intercept by e, I found a value for the work function