= Solution
Near the zone centre, $\cos(k_ia)\simeq1-k_i^2a^2/2$. The <tight-binding model> becomes
$$
E(\mathbf k)\simeq\alpha+6\beta-\beta a^2(k_x^2+k_y^2+k_z^2).
$$
Only $|\mathbf k|^2$ appears at quadratic order, so the <band effective mass> tensor is isotropic. Higher-order lattice terms need not be isotropic.
For the conduction band, $\beta_c<0$, so the curvature is positive and
$$
\boxed{m_c^*=\frac{\hbar^2}{2|\beta_c|a^2}=0.2397m_e.}
$$
Here $a=5.42\times10^{-10}$ m and both beta parameters must be converted from eV to joules. The band edges at the zone centre are
$$
E_v=-1.700+6(0.180)=-0.620\ \mathrm{eV},\qquad
E_c=3.866-6(0.541)=0.620\ \mathrm{eV},
$$
so the model has a \b[direct gap $\boxed{E_g=1.240\ \mathrm{eV}}$]. The mass values describe curvature at these extrema; they are not constant masses throughout the full tight-binding bands.
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