Avogadro’s number of photons

In principle, one molecule of a chemiluminescent reactant can react to form one electronically excited molecule, which in turn can emit one photon of light. Thus one mole of reactant can generate Avogadro s number of photons defined as one einstein (ein). Light yields can therefore be defined in the same terms as chemical product yields, in units of einsteins of light emitted per mole of chemiluminescent reactant. This is the chemiluminescence quantum yield which can be as high as 1 ein/mol or 100%. 

Microwave radiation has a wavelength on the order of 1.0 cm. Calculate the frequency and the energy of a single photon of this radiation. Calculate the energy of an Avogadro s number of photons (called an einstein) of this electromagnetic radiation. 

One mole of photons (Avogadro s number of photons) is called an einstein of radiation. Calculate the energy, in calories, of one einstein of radiation at 3000 A. 

When the energy is in units of kJ mol, this is the energy associated with one mole of photons. Avogadro s constant is the number of formula units in one mole of a substance and so the number of photons in one mole of photons is 6 02 x 10 photons. 

The energy of a photon with frequency v can be calculated with the Planck equation E = hv. To find the energy per mole of photons, the energy of one photon must be multiplied by Avogadro s number. 

T einstein equals Avogadro s number times the energy of one photon of light at the frequency in question. The electronvolt is the kinetic energy acquired by an electron in passing through a potential difference of 1 V in vacuum. 

Instead of energy per photon, we are usually more interested in the energy per Avogadro s number N (the number of molecules per mole, 6.022 x 1023) of photons (N photons is sometimes called an einstein, but the correct SI unit is mole). On a mole basis, Equation 4.2a becomes... 

Further, since 1 mole of photons (defined by modem convention as 1 Einstein) contains N photons (where N is Avogadro s number, 6 x 10 ), then... 

Photon energy can be expressed per mole of a substance by multiplying hv by Avogadro s number, 6.022 x 1023 molecules mol-1 ... 

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