Radiation at 4.2 nm Wavelength: X-Ray Region Frequency & Energy Calculation

Electromagnetic radiation at λ = 4.2 nm falls in the extreme ultraviolet / soft X-ray boundary region.

Calculations

Given: λ = 4.2 nm = 4.2 × 10⁻⁹ m

Constants: c = 2.998 × 10⁸ m/s; h = 6.626 × 10⁻³⁴ J·s

Frequency (f = c/λ)

f = (2.998 × 10⁸) / (4.2 × 10⁻⁹) = 7.14 × 10¹⁶ Hz

Photon Energy (E = hf)

E = (6.626 × 10⁻³⁴) × (7.14 × 10¹⁶) = 4.73 × 10⁻¹⁷ J

In electronvolts: E = (4.73 × 10⁻¹⁷ J) / (1.602 × 10⁻¹⁹ J/eV) = 295 eV

Spectral Classification

• Extreme Ultraviolet (EUV): 10–124 nm (10–124 eV)
• Soft X-rays: 0.1–10 nm (124 eV – 12.4 keV)
• 4.2 nm = 295 eV → Soft X-ray region.

Applications

• EUV lithography (13.5 nm) – semiconductor manufacturing.
• X-ray microscopy / spectroscopy – material science, biology.
• Solar physics: Corona emits strongly in EUV/soft X-ray.
• Medical imaging: Not used diagnostically (poor tissue penetration); research only.

Safety Note

Ionizing radiation (>100 eV). Requires shielding, monitoring in lab/synchrotron settings. Not encountered in routine clinical practice.