Question

7
the microwaves used to heat food have a wavelength of 0.125 m. what is the energy of one photon of the microwave radiation? * (0.5 points)
5.30 x 10^(-33) j
8.28 x 10^(-35) j
3.75 x 10^7 j
1.59 x 10^(-24) j
4.17 x 10^(-10) j
2.40 x 10^9 j
1.88 x 10^32 j

Explanation:

Step1: Recall the energy - wavelength formula

The energy of a photon is given by $E = h
u$, and since $
u=\frac{c}{\lambda}$, then $E=\frac{hc}{\lambda}$, where $h = 6.626\times10^{-34}\ J\cdot s$ (Planck's constant), $c= 3\times 10^{8}\ m/s$ (speed of light) and $\lambda$ is the wavelength.

Step2: Substitute the values

We are given $\lambda = 0.125\ m$, $h = 6.626\times10^{-34}\ J\cdot s$ and $c = 3\times 10^{8}\ m/s$.
\[

$$\begin{align*} E&=\frac{6.626\times 10^{-34}\ J\cdot s\times3\times 10^{8}\ m/s}{0.125\ m}\\ &=\frac{19.878\times 10^{-34 + 8}}{0.125}\ J\\ &=\frac{19.878\times 10^{-26}}{0.125}\ J\\ &=(19.878\div0.125)\times10^{-26}\ J\\ & = 159.024\times10^{-26}\ J\\ &=1.59024\times 10^{-24}\ J\approx1.59\times 10^{-24}\ J \end{align*}$$

\]

Answer:

$1.59\times 10^{-24}\ J$