= Solution
The 110 plane spacing of the conventional cubic cell is
$$
d_{110}(0)=\frac{0.287}{\sqrt2}\ \mathrm{nm}=0.202940\ \mathrm{nm}.
$$
For the first-order Bragg condition,
$$
\sin\theta_0=\frac{\lambda}{2d_{110}}
=\frac{0.154\sqrt2}{2(0.287)}=0.37942\ldots,
\qquad\boxed{2\theta_0=44.596^\circ.}
$$
The quoted experimental deflection is twice the angle between the beam and the reflecting planes; reporting only $22.298^\circ$ would report the <Bragg angle> instead of the requested <Bragg angle>[scattering angle]. The 110 reflection is allowed for the identical-Fe body-centered lattice because $1+1+0$ is even. <Wavelength> and spacing have been expressed in the same units, so their ratio is dimensionless. Higher Bragg orders are conventionally represented by the corresponding higher-index reflection, rather than inserted as an unannounced extra order here.
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