= Solution
{c}
In the <hydrogenic donor state> approximation, the screened <Coulomb potential energy> is $-e^2/(4\pi\epsilon_0\epsilon_r r)$ and the kinetic term uses $m^*=0.067m_e$. Rescaling the <hydrogen atom> gives the <effective Bohr radius of a hydrogenic donor> and the positive binding <energy>
$$
a_b=\frac{4\pi\epsilon_0\epsilon_r\hbar^2}{m^*e^2}
=\frac{12.9}{0.067}a_0,
\qquad
E_b=\frac{\hbar^2}{2m^*a_b^2}
=13.6057\,\mathrm{eV}\frac{0.067}{12.9^2}.
$$
Therefore
$$
\boxed{a_{\rm binding}=10.19\,\mathrm{nm},\qquad E_{\rm binding}=5.48\,\mathrm{meV}.}
$$
The radius here is the exponential length of the ground-state <wavefunction>, not its root-mean-square radius. With $\psi(r)=(\pi a_b^3)^{-1/2}e^{-r/a_b}$, radial integration gives $\langle r^2\rangle=3a_b^2$ and $\langle x^2+y^2\rangle=2a_b^2$.
For dilute independent donors of number <density> $n$, a bound <spin> one-half <electron> has <magnetic moment> magnitude $\mu_s=|g|\mu_B/2$, with the <Bohr magneton> defined using the bare <electron mass>. Its weak-field <Curie law> response is
$$
\chi_{\rm spin}=\frac{\mu_0n g^2\mu_B^2}{4k_BT}.
$$
For the orbital response, expand the <effective mass> <Hamiltonian> $(\mathbf p+e\mathbf A)^2/(2m^*)$ in a uniform <magnetic field>, using $\mathbf A=\mathbf B\times\mathbf r/2$. The spherical ground state has zero orbital <angular momentum>; the quadratic term raises its <energy> by
$$
\Delta E_{\rm orb}=\frac{e^2B^2}{8m^*}\langle x^2+y^2\rangle
=\frac{e^2a_b^2}{4m^*}B^2.
$$
Differentiating this <energy> twice and using $B\simeq\mu_0H$ gives
$$
\chi_{\rm orb}=-\frac{\mu_0ne^2a_b^2}{2m^*}.
$$
The donor-only <magnetic susceptibility> cancels when
$$
\boxed{T_* =\frac{g^2\mu_B^2m^*}{2k_Be^2a_b^2}
=\frac{g^2}{4}\left(\frac{m^*}{m_e}\right)^2\frac{E_b}{k_B}
\simeq1.44\times10^{-2}\,\mathrm K.}
$$
The negative sign of $g=-0.45$ drops out of the linear <magnetic susceptibility>. This crossover is far below $E_b/k_B\simeq63.6\,\mathrm K$, consistent with donor binding. It assumes sufficiently weak <magnetic field>, negligible exchange between donors and a thermal scale above any inter-donor splitting; sufficiently dilute donors can satisfy those assumptions. The background <diamagnetism> from part (b) is excluded from this cancellation.
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