Answer to Question #250030 in Quantum Mechanics for John

Question

Convert the following frequencies to wavelengths (please present the final answer in the most appropriate units to present the quantities in a succinct manner):

a. 10.37 Hz

b. 400.1 MHz

c. 1.91 GHz

d. 79 GHz

e. 167 MHz 

Answer 1

We know that the product of wavelength and frequency is the speed of light

$\lambda \nu = c$ , so $\lambda = \dfrac{c}{\nu}$

a. $\lambda = \dfrac{c}{\nu} = \dfrac{299\, 792\, 458\mathrm{\,m/s}}{ 10.37\,\mathrm{Hz}} = 2.89\cdot10^7\,\mathrm{m} = 28900\,\mathrm{km}.$

b. $\lambda = \dfrac{c}{\nu} = \dfrac{299\, 792\, 458\mathrm{\,m/s}}{ 400.1\cdot10^6\,\mathrm{Hz}} = 0.75\,\mathrm{m} = 75\,\mathrm{cm}.$

c. $\lambda = \dfrac{c}{\nu} = \dfrac{299\, 792\, 458\mathrm{\,m/s}}{ 1.91\cdot10^9\,\mathrm{Hz}} = 0.157\,\mathrm{m} = 15.7\,\mathrm{cm}.$

d. $\lambda = \dfrac{c}{\nu} = \dfrac{299\, 792\, 458\mathrm{\,m/s}}{ 79\cdot10^9\,\mathrm{Hz}} = 3.8\cdot10^{-3}\,\mathrm{m} = 3.8\,\mathrm{mm}.$

e. $\lambda = \dfrac{c}{\nu} = \dfrac{299\, 792\, 458\mathrm{\,m/s}}{ 167\cdot10^6\,\mathrm{Hz}} = 1.80\,\mathrm{m} .$