Question

One type of electromagnetic radiation has a frequency of 107.1 MHz, another type has a wavelength of 2.12 10-10 m, and another type of electromagnetic radiation has photons with energy equal to 3.97 10-19 J/photon. Identify each type of electromagnetic radiation. 107.1 MHz 2.12 10-10 m 3.97 10-19 J/photon FM radiowaves X-rays visible (green) light visible (red) light FM radiowaves X-rays visible (green) light visible (red) light FM radiowaves X-rays visible (green) light visible (red) light Rank them in order of increasing photon energy and increasing frequency

Answer 1

Explanation:

1)

Electromagnetic wave -1

Frequency of an electromagnetic wave -1= $\nu_1= 107.1 MHz$

$107.1 MHz=107.1\times 10^6 hz=1.071\times 10^8 Hz=1.071\times 10^8 s^{-1}$

Wavelength of the electromagnetic wave-1 = $\lambda _1$

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

$\nu =\frac{c}{\lambda _1}$

$\lambda _1=\frac{c}{\nu }$

$\lambda _1=\frac{3\times 10^8 m/s}{1.071\times 10^8 s^{-1}}=2.80m$

(FM-radiowaves)

Electromagnetic wave -2

Wavelength of the electromagnetic wave-2 = $\lambda _2$

$\lambda _2=2.12\times 10^{-10}m=2.12\times 10^{-10}\times 10^9 nm$

$\lambda _2=0.212 nm$ (X-rays)

Electromagnetic wave -3

Wavelength of the electromagnetic wave-3 = $\lambda _3$

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

Planck's constant = h = $6.626\times 10^{-34} Js$

Energy of the photon of the electromagnetic wave-3 =E

E = $3.97\times 10^{-19} J$

$E=\frac{hc}{\lambda _3}$

$\lambda _3=\frac{hc}{E}$

$=\frac{6.626\times 10^{-34} Js\times 3\times 10^8 m/s}{3.97\times 10^{-19} J}$

$\lambda _3=5.0071\times 10^{-7} m=5.0071\times 10^{-7}\times 10^9 nm$

$\lambda _3=500.71 nm$ (visible light)

2) Wavelength of the electromagnetic wave is inversely related to the frequency of the radiations.

$Frequency\propto \frac{1}{Wavelength}$

Decreasing order of wavelength of given waves:

$\lambda _1>\lambda _3>\lambda _2$

Increasing order of wavelength of given waves:

$\nu _1<\nu_3<\nu_2$