Question #02253

Question

1730 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-08T14:59:17

$E = 3.03 \times 10^{- 20}$ $E = 3.03 xx 10^-20$ $J$ $"J"$

We're asked to calculate the energy if a photon given its wavelength.

To do this, we can use the equation

$E = \frac{h c}{λ}$ $E = (hc)/lambda$

where

$E$ $E$ is the energy of the photon, in $J$ $"J"$
$h$ $h$ is Planck's constant, equal to $6.626 \times 10^{- 34}$ $6.626 xx 10^-34$ $J ∙ s$ $"J"•"s"$
$c$ $c$ is the speed of light in vacuum, equal to $299792458$ $299792458$ $m/s$ $"m/s"$
$λ$ $lambda$ is the wavelength of the photon, in $m$ $"m"$

We therefore need to convert from $μm$ $"μm"$ to $m$ $"m"$ :

$6.55cancel("μm")((1color(white)(l)"m")/(10^6cancel("μm"))) = 6.55 xx 10^-6$ $"m"$

Plugging in known values, we have

$E = ((6.626xx10^-34color(white)(l)"J"•cancel("s"))(299792458(cancel("m"))/(cancel("s"))))/(6.55 xx 10^-6cancel("m"))$

$= color(red)(3.03 xx 10^-20$ $color(red)("J"$