You should write the wavelength as °A (Angstroms) and not as a.u. the unit a.u. is used in astronomy and it is very large.
In the single slit experiment of Young, we have the angle Ф of the minimum intensities on the screen with respect to the perpendicular bisector of the slit as:
sin Ф ≈ Ф ≈ n λ / a , n = +- 1, +- 2, +- 3,....
where λ = wavelength of the light wave of single frequency
a = single slit width
hence the angular separation of the first two minima = 2λ/a - λ/a = λ/a
= 5500 * 10⁻⁸ cm / 22 * 10⁻⁵ cm
= 0.25 radians = 14.32 degrees