Determine the change in proton number after alpha emission.

An alpha particle is $_2^4\text{He}$. When a nucleus emits an alpha particle, its proton number (atomic number, Z) decreases by 2.
Initial proton number = 74.
Proton number after alpha emission = $74 - 2 = 72$.

A beta particle (specifically, a beta-minus particle) is $_{-1}^0\text{e}$. When a nucleus emits a beta-minus particle, a neutron converts into a proton, and its proton number (atomic number, Z) increases by 1.
Proton number after alpha emission = 72.
Proton number after beta emission = $72 + 1 = 73$.

The final proton number of the product is 73.

The final answer is $\text{C 73}$.