Answer
The binding energy is $2.84\times 10^7~eV$
Work Step by Step
The mass of an $\alpha$ particle is $4.00151~u$
We can find the mass of two neutrons and two protons:
$M = 2(1.008665~u)+2(1.007276~u)$
$M = 4.031882~u$
We can find the missing mass:
$\Delta m = 4.031882~u-4.00151~u$
$\Delta m = 0.030372~u$
We can assume that the energy of the missing mass is the binding energy:
$E = \Delta m~c^2$
$E = (0.030372~u)(3.0\times 10^8~m/s)^2$
$E = (0.030372)(1.66054\times 10^{-27}~kg)(3.0\times 10^8~m/s)^2$
$E = (4.539\times 10^{-12}~J)(\frac{1~eV}{1.6\times 10^{-19}~J})$
$E = 2.84\times 10^7~eV$
The binding energy is $2.84\times 10^7~eV$
