Question 43.5: Binding Energy of a Deuteron A deuteron is the nucleus of de......
Binding Energy of a Deuteron
A deuteron is the nucleus of deuterium (an isotope of hydrogen, { }_1^2 H), consisting of one proton and one neutron. Use the information in Table 43.2 to find the binding energy of a deuteron. Use no more than six significant figures in your work.
| Table 43.2 Rest mass of selected particles and nuclei | |
| Nucleon or Nucleus | m\left(\text { in } MeV / c^2\right) |
| Proton | 938.27 |
| Neutron | 939.57 |
| Deuteron { }_1^2H | 1875.612859 |
| Helium { }_2^4He | 3727.379 |
| Carbon { }_6^{12}C | 11177.9 |
| Oxygen { }_8^{16}O | 14899.2 |
| Iron { }_{26}^{56}Fe | 52103.06 |
| Copper { }_{29}^{63}Cu | 58603.84 |
| Gold { }_{ 79}^{197}Au | 183433.33 |
| Lead { }_{ 82}^{208}Pb | 193687.68 |
| Uranium { }_{ 92}^{238}U | 221696.64 |
INTERPRET and ANTICIPATE
The mass of a deuteron is less than the mass of a proton plus a neutron. The mass deficit is proportional to the binding energy.
SOLVE
First, find the sum of the masses of the proton and neutron.
Next, find the mass deficit (Eq. 43.15).
Multiply by c² to find the binding energy. Now we see why these pseudo-units are so convenient—the c² cancels out.
\begin{aligned}& E_B=\Delta m c^2=\left(2.23 MeV / c^2\right) c^2 \\& E_B=2.23 MeV\end{aligned}CHECK and THINK
This may not seem like much energy at first, but compare it to the energy required to ionize hydrogen (13.6 eV). The binding energy of a nucleus is about 10^5 times greater than the binding energy of an atom.