Question

1. 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)

3.75 x 10^7 j
2.40 x 10^9 j
4.17 x 10^(-10) j
1.59 x 10^(-24) j
8.28 x 10^(-35) j
5.30 x 10^(-33) j
1.88 x 10^32 j

Explanation:

Step1: Recall 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), $c = 3\times10^{8}\ m/s$ (speed of light), and $\lambda$ is the wavelength.

Step2: Substitute values

Substitute $h = 6.626\times10^{-34}\ J\cdot s$, $c = 3\times10^{8}\ m/s$, and $\lambda=0.125\ m$ into the formula $E=\frac{hc}{\lambda}$.
$E=\frac{6.626\times10^{-34}\times3\times10^{8}}{0.125}$
$E=\frac{19.878\times10^{-34 + 8}}{0.125}=\frac{19.878\times10^{-26}}{0.125}$
$E = 159.024\times10^{-26}\ J=1.59024\times10^{-24}\ J\approx1.59\times10^{-24}\ J$

Answer:

$1.59\times 10^{-24}\ J$ (corresponding to the fourth - option in the multiple - choice list)