Question

1. in each of the following pairs, circle the form of radiation with the longer wavelength:

a. red light or blue light
b. microwaves or radiowaves
c. infrared radiation or red light
d. gamma rays or uv radiation

1. in each of the following pairs, circle the form of radiation with the greater frequency:

a. yellow light or green light
b. x - rays or gamma rays
c. uv radiation or violet light
d. am radio waves or fm radio waves

1. in each of the following pairs, circle the form of radiation with the lower energy:

a. red light or blue light
b. microwaves or radiowaves
c. infrared radiation or red light
d. gamma rays or uv radiation
e. yellow light or green light
f. x - rays or gamma rays
g. uv radiation or violet light
h. am radio waves or fm radio waves

1. springfields \classic rock\ radio station broadcasts at a frequency of 102.1 mhz. what is the length of the radio wave in meters?
2. a beam of light has a wavelength of 506 nanometers. what is the frequency of the light? what color is the light?
3. blue light has a frequency of 6.98 x 10^14 hertz. calculate the wavelength of blue light in nanometers.

Explanation:

Question 4

Step1: Convert frequency to Hz

Given \( f = 102.1\ MHz=102.1\times10^{6}\ Hz\)

Step2: Use the formula \(c = \lambda f\) (where \(c = 3\times10^{8}\ m/s\))

Rearrange for \(\lambda\): \(\lambda=\frac{c}{f}\)
Substitute \(c = 3\times10^{8}\ m/s\) and \(f = 102.1\times10^{6}\ Hz\)
\(\lambda=\frac{3\times 10^{8}}{102.1\times10^{6}}\)
\(\lambda=\frac{300}{102.1}\approx 2.94\ m\)

Step1: Convert wavelength to meters

Given \(\lambda = 506\ nm=506\times10^{-9}\ m\)

Step2: Use the formula \(c=\lambda f\)

Rearrange for \(f\): \(f = \frac{c}{\lambda}\)
Substitute \(c = 3\times10^{8}\ m/s\) and \(\lambda=506\times 10^{-9}\ m\)
\(f=\frac{3\times10^{8}}{506\times10^{-9}}=\frac{3\times10^{17}}{506}\approx5.93\times 10^{14}\ Hz\)
For the color, since \(495 - 570\ nm\) is green - yellow range and \(506\ nm\) is in this range, the color is green.

Step1: Use the formula \(c=\lambda f\)

Rearrange for \(\lambda\): \(\lambda=\frac{c}{f}\)
Given \(c = 3\times10^{8}\ m/s\) and \(f = 6.98\times10^{14}\ Hz\)
\(\lambda=\frac{3\times10^{8}}{6.98\times10^{14}}=\frac{3\times10^{-6}}{6.98}\ m\)
Convert to nanometers: \(\lambda=\frac{3\times10^{-6}}{6.98}\times10^{9}\ nm=\frac{3000}{6.98}\approx429.8\ nm\)

Answer:

The length of the radio - wave is approximately \(2.94\ m\)

Question 5