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? When you input large numbers such as those in
this problem, then input the numbers with parenthesis so as to obtain the correct answer. (b)
Explain why a red light used in a darkroom does not affect the film during developing.

(a) To find the frequency of light needed to bring about the changes in the silver compounds, we can use the equation that relates the energy of a photon to its frequency:

E = hf

Where E is the energy of the photon, h is Planck's constant (6.63 x 10^-34 J⋅s), and f is the frequency of the light.

To solve for the frequency, we can rearrange the equation:

f = E / h

Substituting the given value for the energy of the photon (4.00 x 10^-19 J), and the value of Planck's constant, we get:

f = (4.00 x 10^-19 J) / (6.63 x 10^-34 J⋅s)

Using parentheses to input the large numbers accurately, we can calculate the frequency of the light needed to bring about the changes in the silver compounds.

(b) Red light used in a darkroom does not affect the film during developing because red light has a longer wavelength and lower energy compared to other wavelengths of light such as blue or ultraviolet.

The silver compounds on the film are sensitive to shorter wavelengths and higher energy photons. Red light, with its longer wavelength, does not possess enough energy to trigger the chemical changes in the silver compounds, thus making it safe to use in a darkroom without affecting the film during developing.

This principle is based on the fact that different compounds have different absorption properties based on their structure and composition. In the case of black-and-white film, the silver compounds are specifically designed to be sensitive to certain wavelengths of light, typically in the blue and ultraviolet range. This allows the film to capture images effectively while being processed in the light-sensitive chemicals.