Question

A certain violet light has a wavelength of 413 nm. Calculate the frequency of the light. Calculate the energy content of one quantum of the light.

Answer 1

We will have the following:

First, we transform from nm to m,t that is:

$\lambda=413nm\cdot\frac{m}{1\cdot10^9nm}\Rightarrow\lambda=4.13\cdot10^{-7}m$

Then:

$4.13\cdot10^{-7}m=\frac{3.0\cdot10^8m/s}{f}\Rightarrow f=\frac{3.0\cdot10^8m/s}{4.13\cdot10^{-7}m}$$\Rightarrow f\approx7.26\cdot10^{14}Hz$

So, the frequency of the ligth is approximately 7.26*10^14 Hz.

Now, the energy will be:

$E=(6.63\cdot10^{-34}m^2Kg/s)(7.26\cdot10^{14}/s)\Rightarrow E\approx4.81\cdot10^{-19}m^2Kg/s^2$$\Rightarrow E\approx4.81\cdot10^{-19}m^2Kg/s^2\cdot(J/m^2Kg/s^2))\Rightarrow E\approx4.81\cdot10^{-19}J$

And the energy is approximately 4.81*10^-19 J.