A nucleus containing Z protons has a measured radius of 3.6 fm . If...

The radius of a nucleus is given by the formula:
$R = R_0 A^{1/3}$

Substitute the given values:
$3.6 = 1.2 A^{1/3}$
$A^{1/3} = \dfrac{3.6}{1.2} = 3$

Cubing both sides, we get the mass number:
$A = 3^3 = 27$

The mass defect $\Delta m$ is the difference between the sum of the masses of the constituent nucleons and the rest mass of the nucleus.
Number of protons = $Z$
Number of neutrons = $A - Z = 27 - Z$

Therefore, the mass defect is:
$\Delta m = [Z m_p + (27 - Z) m_n] - M$

Answer: $A = 27$ and $\Delta m = [Z m_p + (27 - Z) m_n] - M$