Electromagnetic Spectrum, Wave Properties, and Photon Energy Calculations

wavelength (λ)

The distance between two consecutive crests or troughs of a wave. Units: meters (m) or nanometers (nm).

frequency (ν)

The number of wave cycles that pass a point per second. Units: Hertz (Hz = 1/s).

frequency and wavelength relationship

They are inversely related — as frequency increases, wavelength decreases.

formula that relates speed, wavelength, and frequency

c=λν, where c=3.00×10^8 m/s.

speed of all EM waves in a vacuum

The speed of light, 3.00×10^8 m/s.

order of the EM spectrum (low → high energy)

Radio → Microwave → Infrared → Visible → Ultraviolet → X-ray → Gamma

EM wave with the longest wavelength

Radio waves.

EM wave with the shortest wavelength

Gamma rays.

EM wave with the highest frequency

Gamma rays.

EM wave with the lowest frequency

Radio waves.

visible light range in nm

About 400-700 nm (Violet → Red).

frequency and energy relationship

Direct — ↑ν → ↑E.

energy and wavelength relationship

Indirect — ↑E → ↓λ.

equation for photon energy using frequency

E=hν

equation for photon energy using wavelength

E=hc/λ

Planck's constant (h)

6.626×10−34 J·s

speed of light (c)

3.00×10^8 m/s

λ = 410 nm → What is ν?

ν=7.32×10^14 Hz

ν = 6.01×10¹⁴ Hz → What is λ?

λ=4.99×10−7 m (499 nm)

ν = 680 kHz → What is λ?

λ=4.41×10^2 m (Radio wave)

ν = 8.0×10¹⁴ Hz → What is λ?

λ=3.75×10−7 m (Violet light)

λ = 4.25×10⁻⁹ m → What is ν?

ν=7.06×10^16 Hz (X-ray)

ν = 8.5×10¹⁴ Hz → What is E?

E=5.63×10−19 J

ν = 5.02×10²⁰ Hz → What is E?

E=3.33×10−13 J (Gamma)

λ = 6.4×10⁻⁷ m → What is E?

E=3.11×10−19 J

λ = 4.06×10⁻¹¹ m → What is E?

E=4.90×10−15 J (X-ray)

λ = 600 nm → What is E?

E=3.31×10−19 J

How to convert nm → m?

Divide by 10^9 (e.g., 500 nm = 5.00×10⁻⁷ m)

How to convert kHz → Hz?

Multiply by 10^3 (e.g., 680 kHz = 6.80×10^5 Hz)