The following masses are known:
$^{1}_{0}$ n 1.008665 u $^{1}_{1}$ H 1.007825 u $^{226}_{88}$ Ra 226.025403 u What is the binding energy of $^{226}_{88}$ Ra?
(1 u = 931.5MeV/c²)

Question

The following masses are known: $^{1}_{0}$n 1.008665 u $^{1}_{1}$ H 1.007825 u $^{226}_{88}$Ra 226.025403 u What is the binding energy of $^{226}_{88}$Ra? (1 u = 931.5MeV/c²)

Quizplus · Accepted Answer

The binding energy can be calculated using the Einstein's famous formula E=mc² where c is the speed of light and m is the mass defect. The mass defect can be found by subtracting the sum of the individual masses of the nucleons from the actual mass of the nucleus.

For $^{226}_{88}$Ra, 
Actual mass = 226.025403 u 
Sum of individual masses = (88 × 1.007825 u) + (138 × 1.008665 u) = 224.982672 u 
Mass defect = Actual mass - Sum of individual masses = 1.042731 u

Now, we can substitute the mass defect into the formula to calculate the binding energy:

E = (1.042731 u) × (931.5 MeV/c²) 
E = 970.044495 MeV

Therefore, the binding energy of $^{226}_{88}$Ra is approximately 970 MeV, which is closest to choice A (1700 MeV).

The Following Masses Are Known 01^{1}_{0}01​ N 1008665 U 11^{1}_{1}11​ H 1007825 U

The Following Masses Are Known $^{1}_{0}$ N 1008665 U $^{1}_{1}$ H 1007825 U