How to calculate frequency and energy

I'm kind of stuck on these 2 questions, can anyone show me how to find the answer please?

What is the energy of light in kilojoules per mole of photons if its frequency is 5.45 x 1014 s-1? (h = 6.626 x 10-34 Js, L = 6.022 x 1023 mol-1)

A surgeon uses a laser with a wavelength of 891.0 nm. What is the frequency of this light? (c = 2.998 x 108 ms-1).

Thanks :)

1.E = hv

E = 6.626 X 10^-34 X 5.45 X 10^14 = 3.611 X 10^-19 J

as 1 kJ = 1000 J
or 1 J = 1/1000 kj

so E = 3.611 X 10^-19 / 1000 kJ = 3.611 X 10^-22 kJ

this is energy due to one photon ....you have to calculate for 1 mole which is 6.022 X 10^23 photons

so E for 1 mole of photn = 3.611 X 10^-22 X 6.022 X 10^23 = 217.454 kJ/mole


2.use this formula ...C = v X wavelenth

where C = speed of light = 2.998 X 10^8 m/s
v = ? s^-1
wavelength = 891 nm = 891 X 10^-9 m

so v = C/wavelength = 2.998 X 10^8 / 891 X 10^-9 = 3.365 X 10^14 s^-1

feel free to ask any question

(1) Firstly, use Planck's relation E=hv where v is the frequency.

E = 6.626E-34 x 5.45E14 = 3.61E-19 J/photon

But you want for one mole of photons: there will be more energy in more photons, so you multiply that by Avogadro's constant (L)

E = 3.61E-19 x 6.022E23 = 2.17E5 J per mole of photons.

Which (dividing by 1000) is about 217kJ/mol (per mole of photons)



(2) You know that for any wave speed = wavelength x frequency.

So in this case 2.998E8 = 891E-9 x frequency

...remembering to keep consistant units. Then just rearrange to get frequency:

frequency = 2.998E8 / (891E-9) = 3.36E14 Hz

yes