Final answer:
The diffraction angle for a single-slit setup with a 2,158 angstrom slit, a minima of order 16, and a wavelength of 8 nm is approximately 36.28 degrees.
Step-by-step explanation:
The question you are asking involves the concept of single-slit diffraction, which is a phenomenon explained by the physics of waves. The formula used to determine the diffraction angle where minima occur in a single-slit experiment is given by:
d sin(θ) = mλ
Where d is the width of the slit, θ is the angle of the diffraction minimum, m is the order of the minimum, and λ is the wavelength of the light. Given that the slit width (d) is 2,158 angstroms (which is 215.8 nm), the order of the minima (m) is 16, and the wavelength (λ) is 8 nm, we use the formula to solve for the angle θ.
215.8 nm * sin(θ) = 16 * 8 nm
Solving for θ gives:
sin(θ) = (16 * 8 nm) / 215.8 nm
θ = arcsin((16 * 8 nm) / 215.8 nm)
θ = arcsin(128 nm / 215.8 nm)
θ = arcsin(0.593)
θ ≈ 36.28° (rounded to two decimal places)
Therefore, the diffraction angle for the given setup, rounded to two decimals, is approximately 36.28 degrees.
J11