Question #6914a

1 Answer
Aug 24, 2016

The wavelength of green light ranges from 492 nm to 597 nm. The frequency ranges from 520 THz to 609 THz.

Explanation:

Here's the spectrum of visible light.

Visible Light
(From www.christianklintholm.com)

The wavelength of green light ranges from 492 nm to 577 nm.

The formula relating frequency and wavelength is

#color(blue)(|bar(ul(color(white)(a/a) fλ=c color(white)(a/a)|)))" "#

where

#f# is the frequency,
#λ# is the wavelength, and
#c# is the speed of light (#2.998 × 10^8color(white)(l) "m·s"^"-1"#).

We can rearrange the formula to get

#color(blue)(|bar(ul(color(white)(a/a) f = c/λcolor(white)(a/a)|)))" "#

We can use this formula to calculate the frequencies at each end of the wavelength range.

At 492 nm,

#f = c/λ = (2.998×10^8 color(red)(cancel(color(black)("m")))"·s"^"-1")/(492×10^"-9" color(red)(cancel(color(black)("m")))) = 6.09 × 10^14color(white)(l) "s"^"-1" = "609 THz"#

At 577 nm,

#f = c/λ = (2.998×10^8 color(red)(cancel(color(black)("m")))"·s"^"-1")/(577×10^"-9" color(red)(cancel(color(black)("m")))) = 5.20 × 10^14color(white)(l) "s"^"-1" = "520 THz"#

∴ The frequency of green light ranges from 520 THz to 609 THz.