GIVEN :-

Interplaner spacing, d = 2.82 A⁰ = 2.82 x 10^-10 m.
Order of spectrum, n = 1

We know that, Bragg's law is 2d sin(theta) = n Lamda
For lamda to be maximum, theta = 90⁰
So, lamda = 2d for first order longest wavelength
So, lamda = 2 x 2.82 A⁰ = 5.64 A⁰