Question

I need help on trying to understand this, please!

Answer 1

The energy will be the same as the speed of light (299792458 m/s) times plank's constant (6.626 x 10^(-34) [J s] all divided by the wavelength [meters].

\[8.86 x 10^{-19} J = \frac{ 299792458 m/s * 6.626 x 10^{-19} J*s }{ Wavelength [m] }\]

Answer 2

1 nm = 10^(-9) m

Answer 3

Well I'm glad I looked up some old notes before saying something silly. Good answer.

Answer 4

The energy \(E\) of a photon of frequency \(f\) is: \[E = hf\]where \(h = 6.626\times10^{-34}\,[\text m^2\cdot\text{kg/s}]\) is plank's constant.

The product of frequency \(f\) and wavelength \(\lambda\), is equal to the velocity of the light,
i.e. \(c = 2.99 8\,[\text{m/s}]\)\[c=f\lambda\]
Solving the second equation for the wavelength \(\lambda\):\[\lambda = c/f\]
Solving the first equation for the frequency \(f\):\[f = E/h\]
Substituting this into the equation for wavelength:\[\lambda = \frac{hc}E\]
Simplifying the constants \[hc = {6.626\times10^{-34}\,[\text J\cdot\text s]\cdot 2.998\times10^8\,[\text {m/s}]}\\
\quad = 1.986\times10^{-25}\,[\text J\cdot \text m]\]
Such that equation for wavelength equation becomes:\[\lambda = \frac{1.986\times10^{-25}\,[\text J\cdot \text m]}E\]
Now just substitute the value for the energy \[E = 8.6\times10^{-19}\,[\text J]\]
(And make your final answer in nanometers; \([\mu\text{m}]=10^{-9}\,[\text m]\).)

Answer 5

@DanJS and @UnkleRhaukus thank you both so much! I can honestly say I understand it now :)