Question

a photon has a wavelength of 553 nm. calculate the energy of the photon in joules. be sure your answer has the correct number of significant digits. note: reference the fundamental constants table for additional information.

Explanation:

Step1: Convert wavelength to meters

The conversion factor is $1\ nm = 1\times10^{- 9}\ m$. So, $\lambda=553\ nm=553\times10^{-9}\ m = 5.53\times10^{-7}\ m$.

Step2: Use the energy - wavelength formula

The energy of a photon is given by $E = h\frac{c}{\lambda}$, where $h = 6.626\times10^{-34}\ J\cdot s$ (Planck's constant) and $c = 3.00\times10^{8}\ m/s$ (speed of light).
Substitute the values: $E=\frac{6.626\times10^{-34}\ J\cdot s\times3.00\times10^{8}\ m/s}{5.53\times10^{-7}\ m}$.

Step3: Calculate the energy

$E=\frac{6.626\times3.00}{5.53}\times10^{-34 + 8+7}\ J=\frac{19.878}{5.53}\times10^{-19}\ J\approx3.6\times10^{-19}\ J$.

Answer:

$3.6\times10^{-19}$