Calculate the nuclear binding energy for a helium-5 atom (isotopic mass = 5.012057 u), a sodium-22 atom (isotopic = 21.99443742 u), and a cobalt-60 atom (isotopic mass = 59.9338222 u)
Calculate the nuclear binding energy for a helium-5 atom (isotopic mass = 5.012057 u), a sodium-22 atom (isotopic = 21.99443742 u), and a cobalt-60 atom (isotopic mass = 59.9338222 u)
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Calculate the nuclear binding energy for a helium-5 atom (isotopic mass = 5.012057 u), a sodium-22 atom (isotopic = 21.99443742 u), and a cobalt-60 atom (isotopic mass = 59.9338222 u)
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Transcribed Image Text:Sample Problem 9
Tritium, H, is the radioactive isotope of hydrogen. It has an isotopic mass of
| 3.0160492 u. What is the binding energy of a tritium atom? What is the binding i
! energy of a mole of tritium atoms?
> First, we need to convert u to kg:
3.0160492 u x 1.66054 × 10-27 kg
Calculating the sum of the individual masses of the nucleons in tritium!
(one proton and two neutrons)
1.6726 x 10-27 kg+ 2(1.6749 x 10-27 kg) = 5.0224 x 10-27 kg
= 5.00827 x 10-27 kg
1 u
Sample Problem 9 cont.
The mass defect is:
Am = 5.0224 x 10-27 kg – 5.00827 x 10-27 kg = 1.413 x 10-29 kg
Solving for the nuclear binding energy:
E = (Am)c2
E, = (1.413 x 10-29 kg) (2.998 x 108) = 1.27 x 10-12)
The value is small, so we usually convert this into megaelectron volts
(MeV).
E, = 1.27 x 10-12 Jx-
> For a mole of tritium atoms:
1 MeV
1.60 x 10-13= 7.94 MeV
E, = 1.27 x 10-12) x 6.022 x 1023 mol-1 = 7.65 x 101.
mol
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