IB Physics HL Theme E: Nuclear and quantum physics questions

A gas is studied using an emission spectrum and an absorption spectrum. For the absorption measurement, the atoms are initially in their lowest energy state. Figure 1 shows the resolved line positions; each line-centre wavelength has an uncertainty of $\pm 2\ \text{nm}$

Assume each line corresponds to a photon transition. Take the lowest atomic energy to be $0\ \text{eV}$ and use $hc=1240\ \text{eV nm}$

A monochromatic X-ray photon scatters from an electron that is initially at rest. Model the interaction as a single photon–electron event, with no energy transferred to the rest of the material. Treat the recoiling electron non-relativistically.

Figure 1 shows the geometry and the measured photon wavelengths. The wavelengths are rounded to the nearest $0.00001\ \mathrm{nm}$

Use $h=6.626\times10^{-34}\ \mathrm{J\,s}$ $c=2.998\times10^8\ \mathrm{m\,s^{-1}}$ and $m_e=9.11\times10^{-31}\ \mathrm{kg}$

A hypothetical nuclear reaction combines nuclei with nucleon numbers 12 and 24 to form a nucleus with nucleon number 36. The combined initial rest mass is $M_i=35.70\,\mathrm{u}$ Use $1\,\mathrm{u}\,c^2=931.5\,\mathrm{MeV}$

Here, $\Delta m$ is the mass equivalent of the increase in total binding energy. What is $\Delta m/M_i$

A neutron initiates the reaction

Each fission releases three neutrons, and on average a fraction $r$ of neutrons from one generation cause a fission in the next, where $0<3r<1$ Let $m_{235}$ $m_{141}$ $m_{92}$ and $m_n$ be the nuclear masses of the indicated species. Which expression gives the expected total energy released by the complete chain?

Figure 1 shows two fission channels with the same products. The masses shown are atomic masses; the electron numbers balance in each reaction. The incident neutron’s kinetic energy is $0.025\ \text{eV}$ Use $1\ \text{u}\,c^2=931.5\ \text{MeV}$