Question

Calculate the energy (in MeV) released when α decay converts uranium 232U (atomic mass = 232.037146 u) into thorium 228Th (atomic mass = 228.028731 u). The atomic mass of an α particle is 4.002603 u.

Answer 1

To solve this problem it is necessary to apply the concepts related to the energy released through the mass defect.

Mass defect can be understood as the difference between the mass of an isotope and its mass number, representing binding energy.

According to the information given we have that the reaction presented is as follows:

$^{232}U_{92} \Rightarrow ^{228}Th_{90}+^4He_2$

The values of the atomic masses would then be:

Th = 232.037146 u

Ra = 228.028731 u

He = 4.0026

The mass difference of the reaction would then be represented as

$\Delta m = 232.037146 u - (228.028731 u + 4.002603 u )$

$\Delta m = 0.005812 u$

From the international measurement system we know that 1 atomic mass unit is equivalent to 931.5 MeV,

$\Delta m = 0.005812 u (\frac{931.5MeV}{1u})$

$\Delta m = 5.414MeV$

Therefore the energy is 5.414MeV