Question

Electromagnetic waves, which include light, consist of vibrations of electric and magnetic fields, and they all travel at the speed of light.
A.) FM radio. Find the wavelength of an FM radio station signal broadcasting at a frequency of 102.5 MHz .
B.) X rays. X rays have a wavelength of about 0.200 nm . What is their frequency?
C.) The Big Bang. Microwaves with a wavelength of 1.20 mm , left over from soon after the Big Bang, have been detected. What is their frequency?
D.) Sunburn. Sunburn (and skin cancer) are caused by ultraviolet light waves having a frequency of around 1.04×1016 Hz . What is their wavelength?
E.) SETI. It has been suggested that extraterrestrial civilizations (if they exist) might try to communicate by using electromagnetic waves having the same frequency as that given off by the spin flip of the electron in hydrogen, which is 1.42 GHz . To what wavelength should we tune our telescopes in order to search for such signals?
F.) Microwave ovens. Microwave ovens cook food with electromagnetic waves of frequency around 2.45 GHz . What wavelength do these waves have?

Answer 1

Answer:

2.92682 m

$1.5\times 10^{18}\ Hz$

250000000000 Hz

$2.88462\times 10^{-8}\ m$

0.21126 m

0.12244 m

Explanation:

c = Speed of light = $3\times 10^8\ m/s$

$\lambda$ = Wavelength

f = Frequency

Wavelength is given by

$\lambda=\dfrac{c}{f}\\\Rightarrow \lambda=\dfrac{3\times 10^8}{102.5\times 10^6}\\\Rightarrow \lambda=2.92682\ m$

The wavelength is 2.92682 m

Frequency is given by

$f=\dfrac{c}{\lambda}\\\Rightarrow f=\dfrac{3\times 10^8}{0.2\times 10^{-9}}\\\Rightarrow f=1.5\times 10^{18}\ Hz$

The frequency is $1.5\times 10^{18}\ Hz$

$f=\dfrac{c}{\lambda}\\\Rightarrow f=\dfrac{3\times 10^8}{1.2\times 10^{-3}}\\\Rightarrow f=250000000000\ Hz$

The frequency is 250000000000 Hz

$\lambda=\dfrac{c}{f}\\\Rightarrow \lambda=\dfrac{3\times 10^8}{1.04\times 10^{16}}\\\Rightarrow \lambda=2.88462\times 10^{-8}\ m$

The wavelength is $2.88462\times 10^{-8}\ m$

$\lambda=\dfrac{c}{f}\\\Rightarrow \lambda=\dfrac{3\times 10^8}{1.42\times 10^{9}}\\\Rightarrow \lambda=0.21126\ m$

The wavelength is 0.21126 m

$\lambda=\dfrac{c}{f}\\\Rightarrow \lambda=\dfrac{3\times 10^8}{2.45\times 10^9}\\\Rightarrow \lambda=0.12244\ m$

The wavelength is 0.12244 m