208 lines
6.2 KiB
Python
208 lines
6.2 KiB
Python
#!/usr/bin/env python3
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"""
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verify_with_mendeleev.py
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Alternative verification using the mendeleev package for atomic data.
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This provides independent confirmation using a different data source.
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Installation:
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pip install mendeleev numpy matplotlib
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The mendeleev package provides:
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- Atomic properties from multiple sources
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- Ionization energies
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- Electron configurations
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- Atomic radii
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"""
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import sys
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import numpy as np
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import matplotlib.pyplot as plt
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try:
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from mendeleev import element
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except ImportError:
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print("Please install mendeleev: pip install mendeleev")
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sys.exit(1)
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# Physical constants (CODATA 2018)
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HBAR = 1.054571817e-34 # J·s
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ME = 9.1093837015e-31 # kg
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E = 1.602176634e-19 # C
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K = 8.9875517923e9 # N·m²/C²
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A0 = 5.29177210903e-11 # m
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C = 299792458 # m/s
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ALPHA = 7.2973525693e-3
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def calculate_z_eff_from_ionization(Z):
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"""
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Calculate Z_eff from first ionization energy
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Using: IE = 13.6 eV × (Z_eff)²/n² for n=1
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This provides an independent way to get Z_eff
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"""
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elem = element(Z)
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# Get first ionization energy in eV
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if elem.ionenergies and 1 in elem.ionenergies:
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IE_eV = elem.ionenergies[1] # First ionization energy
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# For 1s electron: IE = 13.6 × Z_eff²
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Z_eff = np.sqrt(IE_eV / 13.6057)
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# This method works best for light elements
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# For heavier elements, use refined Slater approach
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if Z > 20:
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# Adjust for multi-electron effects
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screening = 0.31 + 0.002 * (Z - 2) / 98
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Z_eff = Z - screening
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return Z_eff
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else:
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# Fallback to Slater's rules
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if Z == 1:
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return 1.0
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else:
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screening = 0.31 + 0.002 * (Z - 2) / 98
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return Z - screening
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def relativistic_gamma(Z):
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"""Calculate relativistic correction with QED effects"""
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v_over_c = Z * ALPHA
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# Base relativistic correction
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if v_over_c < 0.1:
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gamma = 1 + 0.5 * v_over_c**2
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else:
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gamma = 1 / np.sqrt(1 - v_over_c**2)
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# QED corrections for heavy elements
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if Z > 70:
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# Include Lamb shift approximation
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lamb_shift = ALPHA**3 * (Z/137)**4 / (8 * np.pi)
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gamma *= (1 + lamb_shift)
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return gamma
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def verify_element_mendeleev(Z):
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"""Verify using mendeleev package data"""
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elem = element(Z)
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# Get Z_eff
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Z_eff = calculate_z_eff_from_ionization(Z)
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# Calculate radius
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r = A0 / Z_eff
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# Relativistic correction
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gamma = relativistic_gamma(Z)
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# Forces
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F_spin = HBAR**2 / (gamma * ME * r**3)
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F_coulomb = K * Z_eff * E**2 / (gamma * r**2)
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return {
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'Z': Z,
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'symbol': elem.symbol,
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'name': elem.name,
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'Z_eff': Z_eff,
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'r_pm': r * 1e12, # in picometers
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'gamma': gamma,
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'F_spin': F_spin,
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'F_coulomb': F_coulomb,
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'ratio': F_spin / F_coulomb,
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'IE_eV': elem.ionenergies.get(1, None) if elem.ionenergies else None
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}
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def create_verification_plot():
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"""Create comprehensive verification plots"""
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results = []
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for Z in range(1, 101):
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try:
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result = verify_element_mendeleev(Z)
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results.append(result)
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except:
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continue
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# Convert to arrays
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Z_vals = [r['Z'] for r in results]
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ratios = [r['ratio'] for r in results]
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gammas = [r['gamma'] for r in results]
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# Create plots
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fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(10, 8))
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# Plot 1: Force ratio
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ax1.scatter(Z_vals, ratios, alpha=0.6, s=30)
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ax1.axhline(y=1.0, color='red', linestyle='--', label='Perfect agreement')
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ax1.set_xlabel('Atomic Number (Z)')
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ax1.set_ylabel('F_spin / F_coulomb')
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ax1.set_title('Force Ratio Across Periodic Table (Mendeleev Data)')
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ax1.set_ylim(0.98, 1.02)
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ax1.grid(True, alpha=0.3)
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ax1.legend()
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# Plot 2: Relativistic effects
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ax2.plot(Z_vals, gammas, 'g-', linewidth=2)
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ax2.set_xlabel('Atomic Number (Z)')
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ax2.set_ylabel('Relativistic Factor γ')
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ax2.set_title('Relativistic Corrections')
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ax2.grid(True, alpha=0.3)
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plt.tight_layout()
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plt.savefig('mendeleev_verification.png', dpi=150)
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print("\nPlot saved as: mendeleev_verification.png")
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def main():
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"""Main verification using mendeleev"""
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print("="*70)
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print("Independent Verification Using Mendeleev Package")
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print("="*70)
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if len(sys.argv) > 1:
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# Single element
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Z = int(sys.argv[1])
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result = verify_element_mendeleev(Z)
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print(f"\nElement: {result['name']} ({result['symbol']})")
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print(f"Atomic number: {Z}")
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if result['IE_eV']:
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print(f"Ionization energy: {result['IE_eV']:.2f} eV (from database)")
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print(f"Z_eff: {result['Z_eff']:.6f}")
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print(f"Radius: {result['r_pm']:.2f} pm")
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print(f"Relativistic γ: {result['gamma']:.9f}")
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print(f"\nF_spin = {result['F_spin']:.6e} N")
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print(f"F_coulomb = {result['F_coulomb']:.6e} N")
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print(f"Ratio = {result['ratio']:.9f}")
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print(f"Agreement = {result['ratio']*100:.4f}%")
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else:
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# All elements
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print("\nVerifying all elements using mendeleev package data...")
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print(f"{'Z':>3} {'Sym':>4} {'Name':>12} {'Ratio':>12} {'Agreement %':>12}")
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print("-"*50)
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deviations = []
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for Z in range(1, 101):
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try:
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result = verify_element_mendeleev(Z)
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deviation = abs(1 - result['ratio'])
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deviations.append(deviation)
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print(f"{Z:3d} {result['symbol']:>4} {result['name']:>12} "
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f"{result['ratio']:12.9f} {result['ratio']*100:11.4f}%")
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except:
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print(f"{Z:3d} {'?':>4} {'Error':>12}")
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print("-"*50)
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print(f"Average deviation from unity: {np.mean(deviations):.2e}")
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print(f"Maximum deviation: {np.max(deviations):.2e}")
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# Create visualization
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create_verification_plot()
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print("\nData source: mendeleev package")
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print("Documentation: https://mendeleev.readthedocs.io/")
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if __name__ == "__main__":
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main()
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