Sample Work Physics B Unit 6 Photoelectric Effect

Sample Work Physics B Unit 6 Photoelectric Effect

The photoelectric effect remains one of the most compelling demonstrations of quantum theory in introductory physics courses, and a well‑designed sample work physics b unit 6 photoelectric effect experiment helps students connect abstract concepts like photons, work function, and stopping potential to measurable laboratory results. In this article we walk through the theory, typical apparatus, data‑collection procedures, and analysis steps that make up a complete sample work for Unit 6 of an AP Physics B (or equivalent) curriculum. By following the outlined procedure, learners can reproduce historic results, verify Einstein’s photoelectric equation, and gain confidence in interpreting experimental uncertainties.

Introduction

When light shines on a metal surface, electrons may be ejected if the photon energy exceeds a material‑specific threshold. This phenomenon, first explained by Albert Einstein in 1905, laid the foundation for quantum mechanics and earned him the Nobel Prize in Physics. In a typical sample work physics b unit 6 photoelectric effect lab, students measure the kinetic energy of emitted electrons as a function of incident light frequency, plot stopping potential versus frequency, and extract Planck’s constant and the work function from the slope and intercept of the resulting line. The experiment reinforces concepts such as energy quantization, the particle nature of light, and the importance of careful error analysis.

Understanding the Photoelectric Effect ### Core Principles

• Photon Energy: Each photon carries energy (E = h\nu), where (h) is Planck’s constant ((6.626\times10^{-34},\text{J·s})) and (\nu) is the light frequency.
• Work Function ((\phi)): The minimum energy required to liberate an electron from the metal surface; it is characteristic of the material (e.g., (\phi_{\text{Na}} \approx 2.36,\text{eV})).
• Einstein’s Photoelectric Equation:
  [ K_{\max} = h\nu - \phi ] where (K_{\max}) is the maximum kinetic energy of the ejected electron.
• Stopping Potential ((V_s)): The retarding voltage needed to stop the most energetic electrons; related by (K_{\max}=eV_s) ((e) = elementary charge).

Combining these gives the linear relationship used in the lab:
[eV_s = h\nu - \phi \quad \Longrightarrow \quad V_s = \frac{h}{e}\nu - \frac{\phi}{e} ]

Thus, a plot of (V_s) versus (\nu) yields a slope of (h/e) and an intercept of (-\phi/e).

Why Frequency Matters

Below a certain threshold frequency (\nu_0 = \phi/h), no electrons are emitted regardless of light intensity. This contradicts the classical wave prediction that increasing intensity should eventually liberate electrons, highlighting the particle nature of electromagnetic radiation.

Experimental Setup (Sample Work)

A typical sample work physics b unit 6 photoelectric effect apparatus includes the following components:

1. Light Source – A mercury vapor lamp or set of LEDs providing discrete spectral lines (e.g., 365 nm, 405 nm, 436 nm, 546 nm, 579 nm).
2. Monochromator or Filters – To isolate individual wavelengths and ensure monochromatic illumination.
3. Photoelectric Tube – A vacuum photodiode with a known cathode material (often potassium‑coated cesium or sodium). The anode collects emitted electrons.
4. Variable Power Supply – To apply a retarding (stopping) voltage across the tube, measurable with a digital voltmeter.
5. Picoammeter or Electrometer – To detect the photocurrent; the current drops to zero when the stopping potential is reached. 6. Light Intensity Meter – Optional, to verify that intensity does not affect stopping potential (a key check).

The tube is housed in a light‑tight enclosure to prevent stray photons from contributing to the signal. All connections are made with shielded cables to reduce noise.

Procedure Overview

1. Warm‑up the lamp for at least 15 minutes to stabilize output.
2. Select a wavelength using the monochromator; record its nominal value (\lambda) and compute frequency (\nu = c/\lambda) ((c = 2.998\times10^{8},\text{m/s})).
3. Adjust the retarding voltage to zero and measure the baseline photocurrent (I_0).
4. Increase the stopping voltage in small increments (e.g., 0.1 V steps) while monitoring the current.
5. Record the voltage at which the current falls to within the noise floor of the electrometer (typically <0.1 nA). This is (V_s).
6. Repeat for each available spectral line, performing at least three trials per wavelength to assess repeatability.
7. Optional Intensity Check – Vary the lamp intensity (using neutral density filters) and confirm that (V_s) remains unchanged.

Safety notes: never look directly into the UV lamp; use appropriate shielding and wear UV‑protective goggles if necessary.

Data Analysis and Interpretation ### Step‑by‑Step Calculation 1. Convert Wavelength to Frequency

[ \nu = \frac{c}{\lambda} ] Example: for (\lambda = 365,\text{nm}),
[ \nu = \frac{2.998\times10^{8}}{365\times10^{-9}} \approx 8.21\times10^{14},\text{Hz} ]

2. Tabulate (\nu) (Hz) and measured (V_s) (volts).

3. Plot (V_s) (y‑axis) versus (\nu) (x‑axis). 4. Linear Fit – Perform least‑squares regression to obtain slope (m) and intercept (b).

4. Extract Constants

   • Planck’s constant: (h = m \times e)
   • Work function: (\phi = -b \times e)

   Use (e = 1.602\times10^{-19},\text{C}).

5. Uncertainty Propagation – Combine standard errors from the fit with uncertainties in wavelength calibration (typically ±1 nm) and voltage measurement (±0

Data Analysis and Interpretation

Step-by-Step Calculation

1. Convert Wavelength to Frequency
   [ \nu = \frac{c}{\lambda} ] Example: for (\lambda = 365,\text{nm}),
   [ \nu = \frac{2.998\times10^{8}}{365\times10^{-9}} \approx 8.21\times10^{14},\text{Hz} ]

2. Tabulate (\nu) (Hz) and measured (V_s) (volts).

3. Plot (V_s) (y-axis) versus (\nu) (x-axis).

4. Linear Fit – Perform least-squares regression to obtain slope (m) and intercept (b).

5. Extract Constants

   • Planck’s constant: (h = m \times e)
   • Work function: (\phi = -b \times e)

   Use (e = 1.602\times10^{-19},\text{C}).

6. Uncertainty Propagation – Combine standard errors from the fit with uncertainties in wavelength calibration (typically ±1 nm) and voltage measurement (±0.01 V). The combined uncertainty in (V_s) is then used to propagate uncertainty into (h) and (\phi).

Results and Discussion

The linear relationship (V_s = h\nu / e - \phi / e) is expected. The slope of the (V_s) vs. (\nu) plot should be approximately (4.14 \times 10^{-15}) V·s (or 4.14 × 10^{-15} J·C, equivalent to J·V). The y-intercept should be the negative of the work function (\phi) divided by the electron charge (e), typically yielding a value around 2-5 eV for common metals. Deviations from the theoretical slope or intercept, within experimental uncertainty, provide insight into the accuracy of the setup, calibration, and the fundamental constants derived.

Conclusion

This experiment successfully demonstrates the photoelectric effect, confirming Einstein's explanation that light energy is quantized into photons. By measuring the stopping potential (V_s) required to halt photoelectrons emitted from a metal surface for various monochromatic light frequencies, we directly observe the threshold frequency and derive Planck's constant (h) and the metal's work function (\phi). The linear relationship between (V_s) and (\nu) is a cornerstone of quantum mechanics, validating the photon model of light. The careful control of experimental variables, including light intensity, wavelength selection, and shielding, ensures the reliability of the derived constants. This classic experiment remains a fundamental demonstration of quantum phenomena in undergraduate physics laboratories.

Beyond the basic linear fit, a detailed error analysis reveals the dominant contributors to the uncertainty in the extracted constants. The wavelength calibration uncertainty (±1 nm) translates into a frequency error that grows at shorter wavelengths; for 365 nm this corresponds to Δν ≈ ±1.5 × 10¹² Hz, which, when propagated through the slope, yields an uncertainty in h of roughly ±0.03 × 10⁻³⁴ J·s. The voltage measurement uncertainty (±0.01 V) dominates the scatter in the stopping‑potential data, especially near the threshold where Vₛ is small. By weighting each point according to its inverse variance during the least‑squares fit, the influence of low‑voltage points is reduced, improving the robustness of the intercept determination.

Systematic effects such as contact potentials between the photocathode and the measuring circuit, and the finite response time of the electrometer, can shift the apparent intercept. A common practice to mitigate these is to measure the stopping potential with the light blocked (dark current) and subtract this offset from all illuminated readings. Additionally, maintaining the photocathode at a stable temperature (±0.2 °C) minimizes thermionic emission that could otherwise masquerade as a low‑frequency photoelectric signal.

When the analysis is carried out with these refinements, the experimentally obtained slope typically yields h = (6.62 ± 0.04) × 10⁻³⁴ J·s, in agreement with the CODATA value within one standard deviation. The derived work function for a freshly cleaned sodium surface, for example, comes out as φ = 2.36 ± 0.12 eV, consistent with literature values. These results underscore that even a modest undergraduate apparatus, when coupled with careful uncertainty treatment, can reproduce fundamental constants to a few percent.

In summary, the photoelectric‑effect experiment not only provides a vivid illustration of quantized light but also serves as a practical exercise in data analysis, error propagation, and experimental design. By attending to wavelength and voltage uncertainties, correcting for systematic offsets, and applying weighted regression, students can extract Planck’s constant and the work function with confidence, reinforcing the bridge between observable macroscopic measurements and the microscopic quantum world. This hands‑on experience solidifies conceptual understanding and cultivates the analytical skills essential for further investigations in modern physics.