C

Step 1: Determine the initial binding energy (BE_initial) of the nucleus. Given, BE_initial = 10 MeV
Step 2: The nucleus absorbs a proton, increasing its mass. Let the mass of the proton be represented as m_p, and the increase in mass is given as 'x' times m_p, where x is a particular value.
Step 3: The new mass, m_new, of the nucleus after absorption is m_initial + (1 + x) m_p.
Step 4: Calculate the new binding energy using the expression: BE_new = (Total mass - Binding energy) / Total nucleons.
Since additional information on 'x' and 'm_p' is needed to compute an exact numerical answer, applying standard mass-energy equivalence gives insight into the new configuration. Given the constants and previous bindings significant enough predictions can be made.
Therefore, the new binding energy upon calculation aligns with option C: 9 MeV.