(a) What is the wavelength (in meters) of a 93.3 MHz Radio wave frequency? (b) What is the frequency (in Hz) of an x-ray beam with wavelength of 0.0100 nm?
(a) The wavelength of the radio waves broadcast by an FM radio station is
λ=cfλ = \frac{c}{f}λ=fc
c is the speed of light in vacuum
c=3×108 m/sf=93.3 MHz=93.3×106 Hzλ=3×10893.3×106=3.21 mc = 3 \times 10^8 \;m/s \\ f= 93.3 \;MHz = 93.3 \times 10^6\;Hz \\ λ = \frac{3 \times 10^8}{93.3 \times 10^6} = 3.21 \;mc=3×108m/sf=93.3MHz=93.3×106Hzλ=93.3×1063×108=3.21m
(b)
f=cλλ=0.0100 nm=0.01×10−9 mf=3×1080.01×10−9=300×1017=3.0×1019 Hzf= \frac{c}{λ} \\ λ= 0.0100 \;nm = 0.01 \times 10^{-9}\;m \\ f = \frac{3 \times 10^8}{0.01 \times 10^{-9}} = 300 \times 10^{17} \\ = 3.0 \times 10^{19}\;Hzf=λcλ=0.0100nm=0.01×10−9mf=0.01×10−93×108=300×1017=3.0×1019Hz
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