In 1932 Ernest Walton and John Cockcroft verified experimentally Einstein's equation that relates mass and energy - Leaving Cert Physics - Question 12 - 2022

The nuclear reaction can be represented as: $\text{p} + \text{Li-}_7 \rightarrow \text{Be-}_4 + \text{He-}_4$

To convert the mass:

• Given mass of 1H nuclide = 1.007825 u
• Using the conversion factor, where 1 u = 1.66053906660 × 10⁻²⁷ kg,
• The calculation is: $1.007825 \times 1.66053906660 \times 10^{-27} \approx 1.673534 \times 10^{-27} \text{ kg}$

The discrepancy arises because the mass of the 1H nuclide includes the mass of the electron. The mass of the proton is a separate value:

• The proton mass does not account for the electron, hence the value listed in the tables is greater than the value computed from the nuclide mass.

The kinetic energy (E) can be calculated using: $E = qV$, where q is the charge of the proton and V is the potential difference. Therefore,

• Using the known values: $E = (1.602176634 \times 10^{-19}) \times (70000) = 1.12153257 \times 10^{-14} \text{ J}$

The mass lost can be calculated using: $\Delta m = \frac{E}{c^2}$, where c is the speed of light ( $c = 3 \times 10^8 m/s$):

• Therefore, the mass lost: $\Delta m = \frac{1.12153257 \times 10^{-14}}{(3 \times 10^8)^2} = 1.24376 \times 10^{-32} \text{ kg}$

The energy produced equals the energy released due to the mass lost: $E_{produced} = \Delta m \cdot c^2$

• This can be calculated as: $E_{produced} = 1.24376 \times 10^{-32} \times (3 \times 10^8)^2 = 1.120733 \times 10^{-14} \text{ J}$

Using conservation of momentum and energy: $v = \frac{E}{\text{mass}_\alpha}$, where mass of alpha particle approximately equals $4u = 6.64466 \times 10^{-27} \text{ kg}$. So,

• Rearranging gives: $v = \frac{1.12153257 \times 10^{-14}}{6.64466 \times 10^{-27}} \approx 2.13 \times 10^6 m/s$

A proton is classified as a hadron because it is a composite particle made up of quarks, specifically two up quarks and one down quark. Hadrons are particles that interact via the strong force.

A proton is classified as a baryon because it is a type of hadron formed from three quarks. Baryons are characterized by having half-integer spin and are subject to the Pauli exclusion principle, further indicating their composite quark structure.