A certain red light has a wavelength of 680 nm. What is the frequency of the light?

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A certain red light has a wavelength of 680 nm. What is the frequency of the light?

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Answer 1 · 2017-06-30T15:13:53

$f = 4.4 \times 10^{14}$ $f = 4.4 xx 10^14$ $s^{- 1}$ $"s"^-1$

Explanation:

We're asked to convert a given wavelength of a wave to its frequency.

We can use the equation

$λ f = c$ $lambdaf = c$

where

$λ$ $lambda$ (the lowercase Greek letter lambda) is the wavelength of the wave, in meters
$f$ $f$ is the frequency of the wave, in inverse seconds ( $s$ $"s"$ ) or hertz ( $Hz$ $"Hz"$ )
$c$ $c$ is the speed of light in vacuum, precisely $299, 792, 458$ $299,792,458$ $m/s$ $"m/s"$

Since our wavelength must be in units of $m$ $"m"$ , we'll convert from nanometers to meters, knowing that $1$ $1$ $m$ $"m"$ $= 10^{9}$ $= 10^9$ $nm$ $"nm"$ :

$680cancel("nm")((1color(white)(l)"m")/(10^9cancel("nm"))) = color(red)(6.80 xx 10^-7$ $color(red)("m"$

Plugging in known values to the equation and solving for $f$ , we have

$f = c/lambda$

$f = (299792458(cancel("m")/"s"))/(6.80xx10^-7cancel("m")) = color(blue)(4.4 xx 10^14$ $color(blue)("s"^-1) = color(blue)(4.4 xx 10^14$ $color(blue)("Hz"$

rounded to $2$ significant figures.

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A certain red light has a wavelength of 680 nm. What is the frequency of the light?

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