Question

what is the energy of 1 mole of light that has wavelength 400nm?

Answer 1

1 mole of light?

Answer 2

never heard of moles of light

Answer 3

its in my chemistry exam paper, just thought id see if anyone could help me out with it on here!

the options are:
(a) 4.97*10^-28
(b) 4.97*10^-19
(c) 2.99*10^-4
(d) 2.99*10^5

ignoring the mole and just using E=hv and V=c/wavelenth
i keep getting 4.966*10^-17J which is obviously wrong..:(

Answer 4

it is not called mole .it is called photon

Answer 5

it cant be a typo because the question would have been omitted

Answer 6

We use mole in chemistry ! Otherwise, what did you choose as Planck constant value and celerity value ?

Answer 7

plancks constant (printed in the back of the exam paper) 6.626*10^-34 Js

and whats celerity value?

Answer 8

1 mole of light is a bit unusual, but not unheard of. In chemistry a mole of substances is the number of atoms in a specific mass of the material, for example, one mole of carbon is 12 grams.

However, we must remember that one mole is equal to a number, and that is the same as Avogadros number, which is \(N_A=6.0221415 \times 10^{23}\). Therefore the question wants to know what is teh total energy of this number of photons with a wavelength of 400 nm.

In Quantum mechanics a photon of wavelength \(\lambda\) will have an energy of \[E=\frac{hc}{\lambda}\]where h is Planck's constant, and c is the speed of light.

Plugging in numbers we have the energy for one photon is \[E=\frac{6.67\times10^{-34}\times2.998\times10^{8}}{400x10^{-9}}=4.999165 \times10^{-19}\]

So total energy then is the number of photons i.e. one mole) multiplied by the energy fo one photon \[N_A\times E=6.0221415 \times 10^{23}\times4.999165 \times10^{-19}=300949.733\]

I may have used slightly different precision of constants to your level of physics, but the answer is thus \(2.99\times10^5\).

Answer 9

I hope you haven't made the mistake that celerity is in [meter]/[second] and wavelenght in nano-meter

Answer 10

Oops, I used a wrong value of Plancks constant, instead of 6.67 it should be 6.626 (both to times 10 the -34). It wont change the final value too much though. Smack my wrist though for getting it wrong (i was confusing the number with Gravitational Constant I think)

Answer 11

@Fil Rouge, If you mean me making a mistake, all my units are in SI

Answer 12

thank you!

Answer 13

Your welcome Jessicajane

Answer 14

@JonnyMcA, it was not for you ! But it was cleary a problem of calcul and not of method. I don't know we can use mole for a quantity of photon. Yeah why not, I haven't nothing against that !