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Chapter 6: Problem 76

What is the momentum of a 589 -nm yellow photon?

Short Answer

Expert verified
The momentum of a 589-nm yellow photon is \(1.12*10^{-27} kg.m/s\)

Step by step solution

01

Convert Wavelength to Meters

The given wavelength is in nanometers (nm). The SI unit for wavelength is meters (m), so convert the wavelength to meters by multiplying by \(1x10^{-9}\). Hence, \(λ = 589 nm = 589 * 10^{-9} m\).
02

Calculate Frequency

Next, find the frequency of the photon using the speed of light equation \(c = λν\). Rearranging for \(ν\), we get \(ν = c/λ = (3.00*10^{8} m/s) / (589*10^{-9} m) = 5.09*10^{14}\) Hz.
03

Calculate Energy

The energy of a photon \(E\) is given by the equation \(E = hf\). Substituting Planck's constant \(h = 6.626*10^{-34}\) J.s and \(f = 5.09*10^{14} Hz\) into the equation, we calculate \(E = 6.626*10^{-34} J.s * 5.09*10^{14}\) Hz =\(3.37*10^{-19}\) J.
04

Calculate Momentum

Lastly, calculate the momentum \(p\) using the definition of momentum for a photon, \(p=E/c\). Substitute \(E= 3.37*10^{-19}\) J and \(c = 3.00*10^{8} m/s\) into the equation to get \(p = 3.37*10^{-19} J/3.00*10^{8} m/s = 1.12*10^{-27} kg.m/s\).

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