= Solution
The <photon> <wavelength> is $\lambda=hc/E=3.5424\times10^{-11}\,\mathrm m$. The <exact half-period zone radii> for incident <plane waves> are chosen so that the path to the axial focus increases by $\lambda/2$ per zone:
$$
\sqrt{f^2+r_n^2}-f=\frac{n\lambda}{2},\qquad
\boxed{r_n=\sqrt{nf\lambda+\frac{n^2\lambda^2}{4}}\simeq\sqrt{nf\lambda}.}
$$
Transmit alternate zones and block the others, with $r_0=0$. For $f=1.00\,\mathrm{cm}$, $r_1=0.5952\,\mathrm{\mu m}$. The number of zones is a design choice: \b[100 zones give outer <radius> $5.952\,\mathrm{\mu m}$ and outermost width about $29.8\,\mathrm{nm}$]. Adjacent open zones then arrive in <phase> at the principal focus.
\Image[/past-exam-of-the-physics-course-of-the-year-4-of-the-natural-sciences-course-of-the-university-of-cambridge/2012/paper-1-gp2012-zone-plate.png]
{title=Zone-plate geometry}
{description=Original illustrative binary amplitude plate with twelve zones for legibility; the numerical design in the solution uses one hundred zones. Boundary radii follow the derived half-period optical-path condition.}
The blocking material must be sufficiently opaque at 35 keV; no attenuation coefficient or fabrication thickness is specified. A binary <amplitude> plate also has zero-order transmission and other odd-order foci, so an aperture/order stop may be needed. The principal <focal length> is chromatic, varying as $1/\lambda$ for fixed <radii>.
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