Final answer:
To calculate the visible wavelength that produces fourth-order maximum at an angle of 25.0° on a 25,000-line per centimeter diffraction grating, use the formula wavelength = (2 * d * sin(theta)) / n, where d is the spacing between grating lines and n is the order of the maximum.
Step-by-step explanation:
The visible wavelength that has its fourth-order maximum at an angle of 25.0° when projected on a 25,000-line per centimeter diffraction grating can be calculated using the formula for diffraction:
wavelength = (2 * d * sin(theta)) / n
where d is the spacing between the grating lines (1/25000 cm), theta is the angle of the maximum (25.0°), and n is the order of the maximum (4).
Plugging in the values, we get:
wavelength = (2 * (1/25000) * sin(25.0°)) / 4
Calculating this expression gives us the wavelength of visible light that has its fourth-order maximum at the given angle.