In black-and-white photography, a photon energy of about 4.00 x 10-19 J is needed to bring
about the changes in the silver compounds used in the film. (a) What is the frequency of the
light needed to bring about these changes? (b)
Explain why a red light used in a darkroom does not affect the film during developing.
(a) f = (photon energy)/h
(b) For many B/W films, red light photons do not have enough energy to "expose" the film by changing the silver halide molecules. In any case, they are less able to do so.
(a) Oh dear, I'm afraid my jokes might not be able to help you out with this one. To determine the frequency of the light, we can use the equation E = hf, where E is the energy of a photon, h is Planck's constant, and f is the frequency of the light. Rearranging the equation, we have f = E/h. Plugging in the value of E = 4.00 x 10^(-19) J and h = 6.626 x 10^(-34) J·s, we can calculate the frequency. However, I must admit that my comedy skills are far better than my mathematical abilities!
(b) As for why red light used in a darkroom does not affect the film during developing, well, it's because the red light has a lower frequency and longer wavelength compared to the energy needed to affect the silver compounds in the film. The red light doesn't have enough oomph to trigger the chemical changes, so the film remains unharmed. It's like trying to tickle a gorilla with a feather – it's just not going to work!
To solve this problem, we can use the equation relating photon energy (E) to frequency (ν):
E = hν
where E is the energy of the photon, h is the Planck's constant (6.63 x 10^-34 J·s), and ν is the frequency of the light.
(a) To find the frequency of the light needed to bring about the changes in the silver compounds, we can rearrange the equation above:
ν = E / h
Substituting the given values:
ν = (4.00 x 10^-19 J) / (6.63 x 10^-34 J·s)
Calculating this, we get:
ν ≈ 6.04 x 10^14 Hz
Therefore, the frequency of the light needed to bring about these changes is approximately 6.04 x 10^14 Hz.
(b) In a darkroom, red light is often used because it has a longer wavelength and lower frequency compared to blue or ultraviolet light. The silver compounds used in black-and-white photography are not sensitive to red light because the energy of red photons is insufficient to cause the necessary changes in the silver compounds. The energy of red light is lower than that required to excite the silver compounds and bring about the changes in the film. Hence, red light does not affect the film during developing.
To find the frequency of light needed to bring about changes in black-and-white photography, we can use the equation E = hf, where E is the energy of a photon, h is the Planck's constant (6.63 x 10^-34 J·s), and f is the frequency of light.
(a) To find the frequency, we can rearrange the equation to solve for f:
f = E / h
Given the photon energy E = 4.00 x 10^-19 J, we can substitute it into the equation:
f = (4.00 x 10^-19 J) / (6.63 x 10^-34 J·s)
Calculating this, we get:
f ≈ 6.04 x 10^14 Hz (approximately)
So, the frequency of light needed to bring about changes in black-and-white photography is approximately 6.04 x 10^14 Hz.
(b) In a darkroom, red light is used because red light has a longer wavelength and lower energy compared to other visible light colors, such as blue or green. The silver compounds used in black-and-white film are primarily sensitive to light in the blue and ultraviolet regions of the electromagnetic spectrum.
Since the red light has a frequency lower than the required frequency to bring about changes in the silver compounds, it does not have sufficient energy to affect the film during developing. Therefore, red light does not cause any unwanted changes or exposure on the black-and-white film.
In summary, red light is safe to use in a darkroom for developing black-and-white film because its lower frequency and energy make it less likely to cause unintended reactions or exposures on the film.