Question

complete the table to determine the wavelength of each electromagnetic wave when it travels in a vacuum. assume each one moves through a vacuum with a speed of 2.998 x 10^8 meters per second. write your answers in scientific notation rounded to two decimal places. electromagnetic wave frequency (hz) wavelength (m) microwave 2.45 x 10^9 visible light 4.82 x 10^14 x 10^-7 ultraviolet wave 1.84 x 10^16

Explanation:

Step1: Recall the formula

The formula for the speed of an electromagnetic wave is \(c = \lambda
u\), where \(c = 2.998\times10^{8}\text{ m/s}\) (speed of light in vacuum), \(\lambda\) is the wavelength, and \(
u\) is the frequency. So, \(\lambda=\frac{c}{
u}\).

Step2: Calculate the wavelength of the microwave

Given \(
u = 2.45\times 10^{9}\text{ Hz}\), then \(\lambda=\frac{2.998\times 10^{8}}{2.45\times 10^{9}}=\frac{2.998}{2.45}\times10^{8 - 9}\).
\(\frac{2.998}{2.45}\approx1.22\), so \(\lambda = 1.22\times10^{-1}\text{ m}\).

Step3: Calculate the wavelength of visible - light

Given \(
u = 4.82\times 10^{14}\text{ Hz}\), then \(\lambda=\frac{2.998\times 10^{8}}{4.82\times 10^{14}}=\frac{2.998}{4.82}\times10^{8-14}\).
\(\frac{2.998}{4.82}\approx0.62\), so \(\lambda = 6.22\times10^{-7}\text{ m}\).

Step4: Calculate the wavelength of the ultraviolet wave

Given \(
u = 1.84\times 10^{16}\text{ Hz}\), then \(\lambda=\frac{2.998\times 10^{8}}{1.84\times 10^{16}}=\frac{2.998}{1.84}\times10^{8 - 16}\).
\(\frac{2.998}{1.84}\approx1.63\), so \(\lambda = 1.63\times10^{-8}\text{ m}\).

Answer:

Electromagnetic wave	Frequency (Hz)	Wavelength (m)
Visible light	\(4.82\times 10^{14}\)	\(6.22\times 10^{-7}\)
Ultraviolet wave	\(1.84\times 10^{16}\)	\(1.63\times 10^{-8}\)