Input interpretation
photon wavelength
Equation
ν = c/λ | λ | wavelength ν | frequency c | speed of light (≈ 2.998×10^8 m/s)
Units
Input value
frequency | 750 THz (terahertz)
Results
wavelength | 399.7 nm (nanometers) = 1.574×10^-5 inches = 0.3997 µm (micrometers) = 3.997×10^-7 meters
Possible intermediate steps
Calculate the wavelength using the following information: known variable | | ν | frequency | 750 THz Convert known variables into appropriate units using the following: 1 THz = 1×10^12 s^(-1): known variable | | ν | frequency | 7.5×10^14 s^(-1) The relevant equation that relates wavelength (λ) and frequency (ν) is: ν = c/λ ν = c/λ is equivalent to c/λ = ν: c/λ = ν Take the reciprocal of both sides: λ/c = 1/ν Multiply both sides by c: λ = c/ν Substitute known variables and constants into the equation: known variable | | ν | frequency | 7.5×10^14 s^(-1) constant | | c | speed of light | 2.9979×10^8 m/s | : λ = (2.9979×10^8 m/s)/(7.5×10^14 s^(-1)) Separate the numerical part, (2.9979×10^8)/(7.5×10^14), from the unit part, (m/s)/(1/s) = m: λ = (2.9979×10^8)/(7.5×10^14) m Evaluate (2.9979×10^8)/(7.5×10^14): λ = 3.9972×10^-7 m Convert 3.9972×10^-7 m into nm (nanometers) using the following: 1 m = 1×10^9 nm: Answer: | | λ = 399.7 nm