Question

calculate the energy of a photon with wavelength 500 nm using e = hc/λ. show your work to earn credit.

Explanation:

Step1: Identify constants

The Planck - constant $h = 6.63\times10^{-34}\ J\cdot s$, the speed of light $c= 3\times10^{8}\ m/s$. The wavelength $\lambda = 500\ nm=500\times10^{-9}\ m$.

Step2: Substitute values into formula

$E=\frac{hc}{\lambda}$, substituting $h = 6.63\times10^{-34}\ J\cdot s$, $c = 3\times10^{8}\ m/s$ and $\lambda=500\times10^{-9}\ m$ into the formula, we get $E=\frac{6.63\times10^{-34}\times3\times10^{8}}{500\times10^{-9}}$.

Step3: Calculate the result

First, calculate the numerator: $6.63\times10^{-34}\times3\times10^{8}=19.89\times10^{-26}\ J\cdot m$. Then, divide by the denominator: $E=\frac{19.89\times10^{-26}}{500\times10^{-9}}=\frac{19.89}{500}\times10^{-26 + 9}=0.03978\times10^{-17}\ J = 3.978\times10^{-19}\ J$.

Answer:

$3.978\times10^{-19}\ J$