T002-Experimente FS23 - Angewandte Natur - Duplicate

# Import libraries import pandas as pd import matplotlib.pyplot as plt import numpy as np

import pandas as pd import matplotlib.pyplot as plt import numpy as np # Erstellen des Pandas DataFrames measurements_light_intensity = {'Photon density':[0.2, 0.4, 0.6, 0.8, 1.0], 'Photocurrent (pA)':[3.2, 6.4, 9.6, 12.8, 16.0]} data_light_intensity = pd.DataFrame(data=measurements_light_intensity) print(data_light_intensity)

import pandas as pd import matplotlib.pyplot as plt import numpy as np measurements_voltage_sodium = {'Wavelength (nm)':[300, 350, 400, 450, 500], 'Stopping voltage (V)':[1.79, 1.19, 0.75, 0.41, 0.13]} data_voltage_sodium = pd.DataFrame (data=measurements_voltage_sodium) print (data_voltage_sodium)

import pandas as pd from scipy.constants import c, e measurements_voltage_sodium = { 'Wavelength (nm)': [300, 350, 400, 450, 500], 'Stopping voltage (V)': [1.79, 1.19, 0.75, 0.41, 0.13]} data_voltage_sodium = pd.DataFrame(data=measurements_voltage_sodium) data_voltage_sodium["Frequency (Hz)"] = c / (data_voltage_sodium["Wavelength (nm)"] * 3e8) data_voltage_sodium["Kinetic energy (J)"] = e * data_voltage_sodium["Stopping voltage (V)"] print(data_voltage_sodium)

import pandas as pd from scipy.constants import c, e measurements_voltage_sodium = { 'Wavelength (nm)': [300, 350, 400, 450, 500], 'Stopping voltage (V)': [1.79, 1.19, 0.75, 0.41, 0.13]} data_voltage_sodium = pd.DataFrame(data=measurements_voltage_sodium) data_voltage_sodium["Frequency (Hz)"] = c / (data_voltage_sodium["Wavelength (nm)"] * 1.6e-19) data_voltage_sodium["Kinetic energy (J)"] = e * data_voltage_sodium["Stopping voltage (V)"] print(data_voltage_sodium)

data_voltage_sodium.plot(x="Frequency (Hz)", y="Kinetic energy (J)", kind="scatter") plt.xlabel("Frequency (Hz)") plt.ylabel("Kinetic energy (J)") plt.title("Kinetische Energie der Elektronen als Funktion der Frequenz") plt.show()

import numpy as np # Arrays eU und f eU = data_voltage_sodium["Kinetic energy (J)"] f = data_voltage_sodium["Frequency (Hz)"] # Linearen Fit mit polyfit coefficients = np.polyfit(f, eU, 1) m = coefficients[0] # Steigung q = coefficients[1] # y-Achsenabschnitt print("Steigung (m):", m) print("y-Achsenabschnitt (q):", q)

work_function_joules = 2.28 * 1.6e-19 # Annahme eines typischen Werts von 2.28 eV work_function_ev = work_function_joules / 1.6e-19 print("Austrittsarbeit von Natrium in eV:", work_function_ev)

import matplotlib.pyplot as plt import numpy as np # Arrays eU und f aus den experimentellen Daten eU = data_voltage_sodium["Kinetic energy (J)"] f = data_voltage_sodium["Frequency (Hz)"] # Linearen Fit mit polyfit coefficients = np.polyfit(f, eU, 1) m = coefficients[0] # Steigung q = coefficients[1] # y-Achsenabschnitt # Frequenzbereich für den linearen Fit f_range = np.linspace(0, max(f), 100) eU_fit = m * f_range + q # Zusatzarray für den linearen Fit # Plot der experimentellen Daten und des linearen Fits plt.scatter(f, eU, label="Experimentelle Daten", color='blue') plt.plot(f_range, eU_fit, label="Linearer Fit", color='red') # Achsenbeschriftungen plt.xlabel("Frequenz (Hz)") plt.ylabel("Kinetische Energie (J)") # Titel und Legende plt.title("Kinetische Energie der Elektronen als Funktion von Frequenz") plt.legend() # Diagramm anzeigen plt.show()

import pandas as pd import numpy as np # Experimental measurements measurements_voltage_calcium = {'Wavelength (nm)': [200, 250, 300, 330, 350], 'Stopping voltage (V)': [3.311, 2.072, 1.240, 0.871, 0.650]} data_voltage_calcium = pd.DataFrame(data=measurements_voltage_calcium) # Constants c = 2.998E8 # Speed of light in m/s e = 1.602E-19 # Elementary charge in C # Calculate frequency and kinetic energy data_voltage_calcium["Frequency (Hz)"] = c / (data_voltage_calcium["Wavelength (nm)"] * 1E-9) data_voltage_calcium["Kinetic energy (J)"] = e * data_voltage_calcium["Stopping voltage (V)"] # Linear fit lin_fit_voltage_calcium = np.polyfit(data_voltage_calcium["Frequency (Hz)"], data_voltage_calcium["Kinetic energy (J)"], 1) print(f"Linear Fit:\n slope = {lin_fit_voltage_calcium[0]:.2e}\n y-intercept = {lin_fit_voltage_calcium[1]:.2e}") # Work function (Austrittsarbeit) E_A_calcium = -lin_fit_voltage_calcium[1] print(f"Work function = {E_A_calcium:.2f} eV") # Frequency threshold f_g_calcium = -lin_fit_voltage_calcium[1] / lin_fit_voltage_calcium[0] print(f"Frequency threshold = {f_g_calcium:.2e} Hz")

import pandas as pd import numpy as np import matplotlib.pyplot as plt # Experimental measurements measurements_voltage_calcium = {'Wavelength (nm)': [200, 250, 300, 330, 350], 'Stopping voltage (V)': [3.311, 2.072, 1.240, 0.871, 0.650]} data_voltage_calcium = pd.DataFrame(data=measurements_voltage_calcium) # Constants c = 2.998E8 # Speed of light in m/s e = 1.602E-19 # Elementary charge in C # Calculate frequency and kinetic energy data_voltage_calcium["Frequency (Hz)"] = c / (data_voltage_calcium["Wavelength (nm)"] * 1E-9) data_voltage_calcium["Kinetic energy (J)"] = e * data_voltage_calcium["Stopping voltage (V)"] # Linear fit lin_fit_voltage_calcium = np.polyfit(data_voltage_calcium["Frequency (Hz)"], data_voltage_calcium["Kinetic energy (J)"], 1) print(f"Linear Fit Calcium:\n slope = {lin_fit_voltage_calcium[0]:.2e}\n y-intercept = {lin_fit_voltage_calcium[1]:.2e}") # Work function (Austrittsarbeit) E_A_calcium = -lin_fit_voltage_calcium[1] print(f"Work function Calcium = {E_A_calcium:.2f} eV") # Frequency threshold f_g_calcium = -lin_fit_voltage_calcium[1] / lin_fit_voltage_calcium[0] print(f"Frequency threshold Calcium = {f_g_calcium:.2e} Hz") # Plotting plt.figure(figsize=(8, 6)) plt.scatter(data_voltage_calcium["Frequency (Hz)"], data_voltage_calcium["Kinetic energy (J)"], label='Experimental Data (Calcium)') plt.plot(data_voltage_calcium["Frequency (Hz)"], np.polyval(lin_fit_voltage_calcium, data_voltage_calcium["Frequency (Hz)"]), 'r-', label='Linear Fit (Calcium)') plt.xlabel('Frequency (Hz)') plt.ylabel('Kinetic energy (J)') plt.title('Experimental Data and Linear Fits') plt.legend() plt.grid(True) plt.show()