Question

In: Chemistry

Determine the energy of 1.40 mol of photons for each of the following kinds of light....

Determine the energy of 1.40 mol of photons for each of the following kinds of light. (Assume three significant figures.)

A. infrared radiation (1430 nm )

B. ultraviolet radiation (135 nm )

Expert Solution

We can always relate Wavlenegth and Energy per photon via:

Therefore, get first, Energy per photon, then per mol of photon:

E = h c / WL

h = Planck Constant = 6.626*10^-34 J s

c = speed of particle (i.e. light) = 3*10^8 m/s

W = wavelenght in (m) change from nanometers by 10^-9 ratio

E = energy per particle J/photon

Now, calcualte

a)

E = hc/WL

E = (6.626*10^-34)(3*10^8)/(1430*10^-9) = 1.390*10^-19 J/photon

we have, 1.4 mol of photon, or

photons = 1.4*6.022*10^23 = 8.4308*10^23 photons

Etotal = Eper photon * no of photons = 1.390*10^-19 J/photon * 8.4308*10^23 photons

Etotal = ( 1.390*10^-19)( 8.4308*10^23 ) = 117188.12 J = 117.188 kJ --> 3 sig fig --> 1.17*10^2 kJ

b)

similarly:

E = hc/WL

E = (6.626*10^-34)(3*10^8)/(135*10^-9) = 1.47244*10^-18 J/photon

we have, 1.4 mol of photon, or

photons = 1.4*6.022*10^23 = 8.4308*10^23 photons

Etotal = Eper photon * no of photons = 1.47244*10^-18 J/photon * 8.4308*10^23 photons

Etotal = ( 1.47244*10^-18)( 8.4308*10^23 ) = 1241384.7152 J = 1241.38 kJ --> 3 sig fig --> 1.24*10^3 kJ

queen_honey_blossom answered 2 years ago

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