Question

Question #6914a

Answer 1

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.

(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.