Electromagnetic Spectrum Physics Example 2

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Example 2

medium
A photon of ultraviolet light has a wavelength of 200 nm200 \text{ nm}. What is its energy? Use c=3×108 m/sc = 3 \times 10^8 \text{ m/s} and h=6.626×10−34 J sh = 6.626 \times 10^{-34} \text{ J s}.

Solution

  1. 1
    Convert wavelength: 200 nm=2×10−7 m200 \text{ nm} = 2 \times 10^{-7} \text{ m}.
  2. 2
    Frequency: f=cλ=3×1082×10−7=1.5×1015 Hzf = \frac{c}{\lambda} = \frac{3 \times 10^8}{2 \times 10^{-7}} = 1.5 \times 10^{15} \text{ Hz}.
  3. 3
    Photon energy: E=hf=6.626×10−34×1.5×1015=9.94×10−19 JE = hf = 6.626 \times 10^{-34} \times 1.5 \times 10^{15} = 9.94 \times 10^{-19} \text{ J}

Answer

E≈9.94×10−19 JE \approx 9.94 \times 10^{-19} \text{ J}
Photon energy is proportional to frequency. UV photons carry enough energy to damage DNA and cause sunburn, unlike lower-energy visible or infrared photons.

About Electromagnetic Spectrum

The complete continuum of all electromagnetic waves, organized in order of increasing frequency (or decreasing wavelength).

Learn more about Electromagnetic Spectrum →

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Example 4 hard

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