Nanometers measure the length of very small magnitudes, such as wavelengths. A joule, abbreviated as J, is a unit of energy in the metric system. The conversion between nanometers and joules is important in physics because scientists often need to calculate the energy of electromagnetic radiation from the wavelength. To do this, you apply the following formula derived from Planck's equation: Energy = (Planck constant x speed of light) ÷ wavelength.
Identify Planck Constant Value
Retrieve the Planck constant value: 6.626 069 57 x10^-34 J s.
Use Speed of Light Constant
Get the speed of light constant: 299,792,458 m/s.
Multiply Planck by Speed of Light
Multiply the Planck constant by the speed of light. Work out 6.62606957 x10^-34 J s x 299,792,458 m/s = 1,98645 x10^-25 J m.
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Calculate Wavelength in Meters
Divide the wavelength in nanometers by 10^-9 to calculate the value in meters. For example, the wavelength of 500 nm corresponds to 500 ÷ 10^-9 = 5x10^-7 meters (m).
Divide Product of Constants by Wavelength
Divide the product of the constants by the wavelength in meters to calculate the energy in Joules. In this example, the energy is 1,98645 x10^-25 J m ÷ 5x10^-7 m = 3.973 x10-19 J.