Answer
The energy of a photon of radiation is $4.81\times10^{-19}J$.
Work Step by Step
*Strategy:
- First, we would use the formula $\lambda\times\nu = c$ to find out the frequency of this radiation.
- Then, we would use the Planck's theory formula $E=h\times\nu$ to find the energy of a photon of radiation.
$\lambda$ : wavelength of radiation
$\nu$ : frequency of radiation
$c$ : speed of light in a vacuum ($c\approx2.998\times10^8m/s$)
$E$ : the energy of a single quantum (or in this case, photon)
$h$ : Planck constant ($h\approx6.626\times10^{-34}J.s$)
Step 1: Find the known variables
We know the radiation has wavelength of $413nm$; so $\lambda=413nm=4.13\times10^{-7}m$.
Step 2: Find the frequency of this radiation
$\nu=\frac{c}{\lambda}=\frac{2.998\times10^8}{4.13\times10^{-7}}\approx7.259\times10^{14}s^{-1}$
Step 3: Find the energy of a photon of radiation
$E=h\times\nu=(6.626\times10^{-34})\times(7.259\times10^{14})\approx4.81\times10^{-19}J$
