How To Convert Nanometers To Joules

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:

\(E=\frac{hc}{\lambda}\)

1. Identify Planck Constant Value

Retrieve the Planck constant value: h = 6.626 069 57 x10^-34 J s.

2. Use Speed of Light Constant

Get the speed of light constant: c = 299,792,458 m/s.

3. Multiply Planck by Speed of Light

Multiply the Planck constant by the speed of light. Work out:

\(hc=6.62606957 \times 10^{-34}\times 299,792,458 = 1.98645 \times 10^{-25}\text{ Jm}\)

4. Calculate Wavelength in Meters

Divide the wavelength in nanometers by 10⁹ to calculate the value in meters. For example, the wavelength of 500 nm corresponds to:

\(\frac{500}{10^9}=5\times 10^{-7}\text{ m}\)

5. 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:

\(E=\frac{1.98645\times 10^{-25}}{5\times 10^{-7}}=3.973\times 10^{-19}\text{ J}\)