Question

q 25. how much energy is produced from from a em wave if the wavelength is 2.50 x 10^(-9) meters? q 5.52 x 10^(-51) joules q 5.52 x 10^(-21) joules q 7.95 x 10^(-17) joules q 2.34 x 10^(-24) joules clear all

Explanation:

Step1: Recall energy - wavelength formula

The energy of a photon of an electromagnetic wave is given by $E = \frac{hc}{\lambda}$, where $h = 6.63\times10^{-34}\text{ J}\cdot\text{s}$ (Planck's constant), $c = 3\times 10^{8}\text{ m/s}$ (speed of light in vacuum), and $\lambda$ is the wavelength.

Step2: Substitute the values

Substitute $h = 6.63\times10^{-34}\text{ J}\cdot\text{s}$, $c = 3\times 10^{8}\text{ m/s}$, and $\lambda=2.50\times 10^{-9}\text{ m}$ into the formula:
\[

$$\begin{align*} E&=\frac{6.63\times 10^{-34}\text{ J}\cdot\text{s}\times3\times 10^{8}\text{ m/s}}{2.50\times 10^{-9}\text{ m}}\\ &=\frac{6.63\times3\times10^{-34 + 8}}{2.50\times 10^{-9}}\text{ J}\\ &=\frac{19.89\times10^{-26}}{2.50\times 10^{-9}}\text{ J}\\ &=(19.89\div2.50)\times10^{-26+9}\text{ J}\\ & = 7.956\times10^{-17}\text{ J}\approx7.95\times 10^{-17}\text{ J} \end{align*}$$

\]

Answer:

$7.95\times 10^{-17}$ Joules