Answer to Question #71810 in Organic Chemistry for Rubie Jane Cahilig

Question

5. Calculate the wavelength in centimeters of
a. An airport tower transmitting at 118.6 MHz
b. A VOR (radio navigation aid) transmitting at 114.10 kHz
c. An NMR signal at 105MHz
d. An infrared absorption peak with a wavenumber of 1210 cm

Answer 1

The wavelength: λ = v / f, where:
v - speed of the wave
f - frequency
For electromagnetic waves: v = 3∙108 m/s, therefore:
a. Wavelength = 3∙108 / 1.186∙108 = 2.53 m = 253 cm
b. Wavelength = 3∙108 / 1.141∙105 = 2629 m = 262900 cm
c. Wavelength = 3∙108 / 1.05∙108 = 2.86 m = 286 cm
The wavenumber (in spectroscopy): ṽ = 1 / λ
so: λ = 1 / ṽ
d. Wavelength = 1 / 1210 = 0.000826 cm