Question

2.) a beam of microwaves has a frequency of 1.0 x 10^9 hz. a radar beam has a frequency of 5.0 x 10^11 hz. which type (microwave or radar)... (a)has a longer wavelength? (b) is closer to visible light on the em spectrum? (c) is closer to x - rays in frequency value? 3.) what is the frequency of an em radiation wave if its wavelength is 3.6 x 10^-9 meters? 4.) a beam of em radiation has a wavelength of 4.257 x 10^-7 cm. what is its frequency? 5.) a photon of light has a wavelength of 3.20 x 105 meters. find... (a)the frequency

Explanation:

Step1: Recall the wave - speed formula

The speed of an electromagnetic wave is given by $c = \lambda f$, where $c = 3\times10^{8}\ m/s$ (speed of light in vacuum), $\lambda$ is the wavelength and $f$ is the frequency. So, $\lambda=\frac{c}{f}$.

Step2: Compare wavelengths for part (A)

For microwaves, $f_{1}=1.0\times 10^{9}\ Hz$, then $\lambda_{1}=\frac{3\times 10^{8}}{1.0\times 10^{9}} = 0.3\ m$. For radar, $f_{2}=5.0\times 10^{11}\ Hz$, then $\lambda_{2}=\frac{3\times 10^{8}}{5.0\times 10^{11}}=6\times 10^{-4}\ m$. Since $0.3\ m>6\times 10^{-4}\ m$, microwaves have a longer wavelength.

Step3: Know the order of EM - spectrum for part (B)

The order of the EM - spectrum from lower to higher frequency is: radio waves, microwaves, infrared, visible light, ultraviolet, X - rays, gamma rays. Visible light has frequencies in the range of $4.3\times 10^{14}-7.5\times 10^{14}\ Hz$. The frequency of microwaves is $1.0\times 10^{9}\ Hz$ and of radar is $5.0\times 10^{11}\ Hz$. Radar is closer to visible light in frequency.

Step4: Compare with X - rays frequency for part (C)

X - rays have frequencies in the range of $3\times 10^{16}-3\times 10^{19}\ Hz$. Radar with $f = 5.0\times 10^{11}\ Hz$ and microwaves with $f = 1.0\times 10^{9}\ Hz$. Radar is closer to X - rays in frequency value.

Step5: Calculate frequency for part 3

Given $\lambda = 3.6\times 10^{-9}\ m$, using $f=\frac{c}{\lambda}$, we have $f=\frac{3\times 10^{8}}{3.6\times 10^{-9}}\approx8.33\times 10^{16}\ Hz$.

Step6: Convert wavelength to SI unit for part 4

The wavelength is $\lambda = 4.257\times 10^{-7}\ cm=4.257\times 10^{-9}\ m$. Then $f=\frac{c}{\lambda}=\frac{3\times 10^{8}}{4.257\times 10^{-9}}\approx7.05\times 10^{16}\ Hz$.

Step7: Calculate frequency for part 5(A)

Given $\lambda = 3.20\times 10^{5}\ m$, then $f=\frac{c}{\lambda}=\frac{3\times 10^{8}}{3.20\times 10^{5}} = 937.5\ Hz$.

Answer:

(A) Microwaves
(B) Radar
(C) Radar

1. $8.33\times 10^{16}\ Hz$
2. $7.05\times 10^{16}\ Hz$

5(A). $937.5\ Hz$