Question

Mention the most important conclusion of Rutherford's alpha-particle scattering experiment. Define isotopic, isobaric, and isotonic nuclei. Find the energy equivalent to one atomic mass unit in joules and MeV (1 u = 1.6605 × \(10^{-27}\) kg).

Hint:

Remember, the energy equivalent of mass is given by \(E = mc^2\), and one atomic mass unit is the mass of a carbon-12 atom divided by 12. Always use this formula to convert mass to energy.

Answer 1

Rutherford's Alpha-Particle Scattering Experiment:
In 1909, Ernest Rutherford conducted the famous alpha-particle scattering experiment, in which a beam of alpha particles was directed at a thin gold foil. The most important conclusion from this experiment was the discovery of the atomic nucleus. Rutherford found that most of the alpha particles passed straight through the foil, but a small fraction were deflected at large angles, and some even bounced back. This indicated that the mass of an atom is concentrated in a tiny, dense nucleus at the center, with the rest of the atom being mostly empty space. This led to the development of the Rutherford model of the atom, where electrons orbit around a dense nucleus.
Definitions:
sotopic Nuclei: Nuclei that have the same number of protons but different numbers of neutrons, and thus different atomic masses. For example, \(^1H\) (hydrogen) and \(^2H\) (deuterium) are isotopes of hydrogen.
Isobaric Nuclei: Nuclei that have the same mass number (total number of protons and neutrons) but different numbers of protons (and hence different elements). For example, \(^4He\) and \(^4Be\) are isobars.
Isotonic Nuclei: Nuclei that have the same number of neutrons but different numbers of protons (and thus different elements). For example, \(^4He\) and \(^5Li\) are isotonic nuclei.
Energy Equivalent of One Atomic Mass Unit (1 u):
The energy equivalent of one atomic mass unit can be found using Einstein's famous equation: \[ E = mc^2 \] Where:
- \(m\) is the mass of 1 atomic mass unit (1 u = \(1.6605 \times 10^{-27}\) kg),
- \(c\) is the speed of light (\(3 \times 10^8\) m/s).
First, calculating the energy in joules: \[ E = (1.6605 \times 10^{-27} \, \text{kg}) \times (3 \times 10^8 \, \text{m/s})^2 = 1.49445 \times 10^{-10} \, \text{J} \] Now, converting this energy to MeV (1 J = \(6.242 \times 10^{12}\) MeV): \[ E = 1.49445 \times 10^{-10} \, \text{J} \times 6.242 \times 10^{12} \, \text{MeV/J} = 9.33 \, \text{MeV} \] Thus, the energy equivalent of one atomic mass unit is approximately 1.494 \times \(10^{-10}\) joules or 9.33 MeV.