Engineering
Planck Photon Energy (1239.84 / lambda_nm) & Bragg X-Ray Diffraction Law
Convert optical/LED wavelength in nanometers directly to photon energy in electron-volts (eV) and solve Bragg's Law d = n*lambda / (2*sin(theta)) for crystal d-spacing.
Two indispensable spectroscopy & semiconductor physics formulas in spreadsheet units!
Photon energy is hc divided by vacuum wavelength. The numerical value 1239.84 eV*nm is a rounded conversion constant, not exact. At 500 nm it gives 2.4797 eV to the displayed precision. Wavelength in a medium is not interchangeable with vacuum wavelength.
Bragg geometry gives n*lambda=2*d*SIN(theta), where theta is the glancing angle to the lattice plane, not the angle to its normal. For the positive diffraction orders used here require integer n>=1 and 0<theta<=90 degrees. Instruments often report 2*theta; halve that value before entering B6.
The computed spacing is a geometric condition, not proof of a permitted or measurable reflection. The photon-energy result alone does not establish absorption efficiency or device performance. This article covers photons and Bragg diffraction, not matter-wave de Broglie calculations.
| Quantum / XRD Calculation | Formula / Inputs | Lab Measurement | Calculated Output |
|---|---|---|---|
| 500 nm Green Photon Energy | B3 / B2 (1239.84 / 500) | hc = 1239.84 eV*nm | 2.4797 eV |
| 250 nm Deep-UV Photon | B2 set to 250 nm | Half wavelength -> 2x energy | 4.9594 eV |
| Bragg XRD Lattice Spacing d | (B5 * B4) / (2 * SIN(RADIANS(B6))) | n=1, Cu Ka=0.154 nm, theta=15 deg | 0.2975 nm (2.975 Angstroms) |
| Normal Backscatter (90 deg) | B6 set to 90 deg | SIN(90 deg) = 1 -> lambda / 2 | 0.0770 nm minimum d-spacing |
Planck-Einstein Photon Energy E (eV) = 1239.84 / Wavelength_nm
Use positive vacuum wavelength in nm and the stated rounded hc constant in eV*nm.
=IF(COUNT(B2:B3)<>2,"Invalid inputs",IF(OR(B2<=0,B3<=0),"Invalid inputs",ROUND(B3 / B2, 4)))Bragg X-Ray Diffraction Crystal d-Spacing d = (n * lambda) / (2 * SIN(RADIANS(theta)))
Note that XRD diffractometers often plot 2*theta—be sure B6 holds glancing half-angle theta in degrees!
=IF(COUNT(B4:B6)<>3,"Invalid inputs",IF(OR(B4<=0,B5<1,B5<>INT(B5),B6<=0,B6>90),"Invalid inputs",ROUND((B5 * B4) / (2 * SIN(RADIANS(B6))), 4)))Try the example
Use the original values or change them to test your understanding.