In 1932 J.D - Leaving Cert Physics - Question 10 - 2013

Detection of the alpha-particles was performed using scintillators that emitted flashes of light when struck by the particles. This light was further captured with a zinc sulfide screen, which aided in visualizing the alpha-particles.

The nuclear reaction can be represented as:

$\mathrm{^6_3Li + ^1_1p \rightarrow ^4_2He + ^3_1H}$

The historical significance lies in it being the first experimental verification of the equation $E=mc^2$ and the first artificial splitting of the nucleus, leading to the discovery of transmutation using artificially accelerated particles, which later garnered them the Nobel Prize.

The kinetic energy of the proton is given as 700 keV, which can be converted to joules:

$700 \text{ keV} = 700 \times 1.6 \times 10^{-19} \text{ J} = 1.12 \times 10^{-13} \text{ J}$

Using the formula for kinetic energy, where:

$E = \frac{1}{2} mv^2,$

Rearranging gives:

$v = \sqrt{\frac{2E}{m}}$

Taking the proton mass as $m = 1.67 \times 10^{-27}$ kg, we can calculate:

$v = \sqrt{\frac{2 \times 1.12 \times 10^{-13}}{1.67 \times 10^{-27}}} \approx 1.16 \times 10^7 \text{ m/s}$

The tube is evacuated to create a vacuum, which prevents particles from colliding with gas molecules. This increases the mean free path of the accelerated particles and allows them to travel without interference, ensuring higher energy transfers and more efficient collisions with the target.

Particles are accelerated to high velocities to increase their kinetic energy, allowing them to overcome the Coulomb barrier that exists between positively charged nuclei. Higher velocities ensure sufficient energy for the particles to collide and induce nuclear reactions.

Magnets are used in circular accelerators to bend the paths of charged particles. This bending allows particles to maintain circular orbits within the accelerator, enabling them to recirculate and gain more energy with each pass through the acceleration segments.

A significant advantage of a circular accelerator is its ability to accelerate particles to higher energies. As particles traverse the same path multiple times, they can be accelerated repeatedly, making it possible to achieve a greater final energy than a linear accelerator would allow.

An accelerator of this design cannot effectively accelerate neutrinos because neutrinos are electrically neutral and interact very weakly with matter. Unlike charged particles that can be manipulated with electric and magnetic fields in accelerators, neutrinos would pass through most structures without interaction, making it impractical to accelerate them using conventional methods.