= Solution
The <X-ray> <wavelength> is $\lambda=hc/E=1.54980\times10^{-10}\,\mathrm m$. Write the amplitude of one conventional <unit cell> as the <face-centred cubic selection rule> times the two-atom <atomic basis> amplitude:
$$
F_{hkl}=\left[1+e^{i\pi(k+l)}+e^{i\pi(h+l)}+e^{i\pi(h+k)}\right]
\left[f_{\mathrm{Ga}}+f_{\mathrm{As}}e^{i\pi(h+k+l)/2}\right].
$$
The first bracket is four when the indices have equal parity and zero otherwise. Among the allowed <Bragg reflections>, the <zinc blende structure factor> therefore gives
$$
|F_{hkl}|^2=16\begin{cases}
f_{\mathrm{Ga}}^2+f_{\mathrm{As}}^2,&h,k,l\text{ odd},\\
(f_{\mathrm{Ga}}+f_{\mathrm{As}})^2,&h+k+l\equiv0\pmod4,\\
(f_{\mathrm{Ga}}-f_{\mathrm{As}})^2,&h+k+l\equiv2\pmod4.
\end{cases}
$$
Here the <atomic scattering factors> are taken as real. For the requested rough estimate set $f_{\mathrm{Ga}}\simeq31$ and $f_{\mathrm{As}}\simeq33$. The weak difference reflections remain allowed: unequal species do not have the extra exact extinction of the equal-species diamond limit.
The first six allowed values of $h^2+k^2+l^2$ are $3,4,8,11,12,16$. <Bragg's law> gives the measured scattering angle $2\theta=2\sin^{-1}(\lambda\sqrt{h^2+k^2+l^2}/2a)$. For <powder diffraction>, multiply the squared amplitude by the <powder diffraction multiplicity> $m_{hkl}$. The last two columns use $I_{111}=100$:
$$
\begin{array}{c|r|r|r|r|r}
hkl&2\theta\ ({}^\circ)&m_{hkl}&|F|^2&I\propto m|F|^2&I\propto m|F|^2LP\\\hline
111&27.4693&8&32800&100&100\\
200&31.8234&6&64&0.1463&0.1068\\
220&45.6248&12&65536&299.707&98.684\\
311&54.0830&24&32800&300&67.110\\
222&56.6994&8&64&0.1951&0.03921\\
400&66.5025&6&65536&149.854&21.165
\end{array}
$$
The first intensity column is the geometry-independent multiplicity-and-structure estimate. The second additionally assumes an unpolarized beam and a common symmetric powder-diffractometer geometry, with <Lorentz-polarization factor>
$$
LP(\theta)\propto\frac{1+\cos^2(2\theta)}{\sin^2\theta\cos\theta}.
$$
An overall constant cancels in either normalization. A particular measured intensity set is not fixed by the atomic numbers alone: actual <atomic scattering factors> decrease with momentum transfer, anomalous scattering and absorption can matter, and the instrument geometry and <polarization> determine angular corrections. The two columns state the approximation rather than asserting identical peak heights for all instruments.<Quantitative powder diffraction using a (2 + 3) surface diffractometer and an area detector by Giuseppe Abbondanza and others>[Section 4, equation 5 and sections 4.1–4.2: multiplicity, structure amplitude and geometry-dependent polarization and Lorentz corrections]{ref}
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