What is the energy, in joules, of 1.0 mol of photons of green light?
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Frequency = speed of light/wavelength
F = 3×10^8/5×10^7 = 6×10^14 Hz
Energy = Planks Constant x frequency
E= 6.63×10^34 * 6×10^14 = 3.978×10^19 which is roughly equal to 4×10^19 J for the energy of 1 photon of green light.
4×10^19 x 6.02×10^23 (Avogadro’s Number) = 240800 J per mole of photons of green light. This is 240000 J per mole when rounded to 2 s.f. as given in the question.
To solve this, you would use the formulas c=(lambda)v and E=hv.
First you would plug in 5.0 x 10^7 m into the first equation and solve for v, the frequency.
3.0×10^8 m/s = (5.0×10^7 m)v
Once you solved for v, you would plug that into the equation E=hv, and solve for E. (By the way, the units for v is per seconds, or s^1.)
E=(6.636×10^34 J/s)(your answer for v s^1)
h is Planck’s constant.
This would give you the answer for one photon, and multiplying that by 6.02×10^23 would give you the answer for one mole.
Hope this helps!
E=h*nu
c=nu*lambda
where h is plancks constant(m2 kg/s2), nu is frequency(1/m), lambda is wavelength (m), and E (J). that’s for one photon, so then just multiply by avogadro’s #.