The light-sensitive substance in black-and-white...

The light-sensitive substance in black-and-white photographic film is AgBr. Photons provide the energy necessary to transfer an electron from $\mathrm{Br}^{-}$ to $\mathrm{Ag}^{+}$ to produce elemental $\mathrm{Ag}$ and $\mathrm{Br}$ and thereby darken the film. (a) If a minimum energy of $2.00 \times 10^{5} \mathrm{~J} / \mathrm{mol}$ is needed for this process, what is the minimum energy needed from each photon? (b) Calculate the wavelength of the light neces- (c) Explain why sary to provide photons of this energy. this film can be handled in a darkroom under red light.

The light-sensitive substance in black-and-white photographic film is AgBr. Photons provide the energy necessary to transfer an electron from $\mathrm{Br}^{-}$ to $\mathrm{Ag}^{+}$ to produce elemental $\mathrm{Ag}$ and $\mathrm{Br}$ and thereby darken the film. (a) If a minimum energy of $2.00 \times 10^{5} \mathrm{~J} / \mathrm{mol}$ is needed for this process, what is the minimum energy needed from each photon?
(b) Calculate the wavelength of the light neces-
(c) Explain why sary to provide photons of this energy. this film can be handled in a darkroom under red light.

Key Concepts

Energy per Mole vs. Energy per Photon Conversion

In many photochemical problems, energy is given per mole (in joules per mole), but reactions occur on a per-photon level. Converting from J/mol to the energy of a single photon involves dividing by Avogadro's number. This conversion is crucial for comparing the energy of individual photons with the energy required to initiate a chemical change.

Planck’s Equation and Photon Wavelength

Planck’s equation (E = hc/?) establishes that a photon’s energy is inversely proportional to its wavelength, with h being Planck’s constant and c the speed of light. This relationship is fundamental in linking the energy necessary for a photochemical reaction to the specific wavelength of light that can provide that energy.

Photochemical Reaction Threshold and Spectral Sensitivity

Photochemical processes require photons of sufficient energy to induce a reaction, implying that only light with wavelengths shorter than a certain threshold can trigger the process. In photographic film, if the energy required for a reaction is higher than what red photons can provide, the film remains unexposed under red light, allowing it to be safely handled in a darkroom.

Transcript

00:01 Silver bromide is the light sensitive substance in black and white photography.

00:06 Photons provide the energy necessary to transfer an electron from bromide ion to silver to produce elemental silver and bromine and darken the film.

00:17 So real quickly, photons provide the energy, there's energy, to transfer an electron from br minus to ag plus.

00:46 We get elemental ag and br, and that darkens the film.

01:05 A, if a minimum energy of 2 .00 times 10 to the 5th joules per mole is needed for this process, what's the minimum energy needed for each photon? this one's pretty simple.

01:37 I'm just going to set this up.

01:38 We're just using alvigadro's number here.

01:40 We've got 2 .00 times 10 to the 5th joules per mole, and we know that one mole contains 6 .022 times 10 to the 23rd photons, which equals 3 .321 times 10 to the minus 19th joules per photon.

02:13 And to correct sig figs, that would be 3 .32 times 10 to the minus 19th joules per photon.

02:22 That's part a.

02:26 Part b asks us to calculate the wavelength.

02:33 Calculate the wavelength necessary to produce, provide photons of this energy.

02:47 In order to do that, we're going to use this relationship.

02:51 Energy equals plunks constant times c divided by lambda.

02:56 Rearranging for wavelength, we get wavelength equals plunks constant times c divided by energy.

03:03 We've got all three of those values.

03:07 And once we have that energy, we're to multiply that number by our jewels per photon...

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