Question

An \(\alpha\) particle produced in radioactive \(\alpha\) decay has a kinetic energy of typically about 6 MeV. When an \(\alpha\) particle passes through matter (e.g., biological tissue), it makes ionizing collisions with molecules, giving up some of its kinetic energy to supply the binding energy of the electron that is removed. If a typical ionization energy for a molecule in the body is around \(20 \mathrm{eV}\) roughly how many molecules can the alpha particle ionize before coming to rest?

Short answer

Answer: The alpha particle can ionize approximately \(3 \times 10^5\) molecules in biological tissue.

Step-by-step solution

Convert energies to the same unit

Both energies are given in different units: MeV for the kinetic energy of the alpha particle and eV for the ionization energy. We need to convert one of them to have the same units. In this case, we'll convert the alpha particle's initial energy into eV. 1 MeV equals 1 million eV, so the alpha particle's kinetic energy is: \(6 \mathrm{MeV} = 6 \times 10^6 \mathrm{eV}\)

Calculate the number of ionized molecules

Now that we have the same unit for both energies, we will divide the total kinetic energy of the alpha particle by the ionization energy per molecule to find the approximate number of molecules that can be ionized. Number of ionized molecules = \(\frac{6 \times 10^6 \mathrm{eV}}{20 \mathrm{eV}}\)

Solve for the number of ionized molecules

Dividing the numbers from Step 2, we get the number of ionized molecules as: Number of ionized molecules = \(\frac{6 \times 10^6}{20} = 3 \times 10^5\) The alpha particle can ionize approximately \(3 \times 10^5\) molecules before coming to rest in the biological tissue.