Structure Of Atom (Discovery of Sub-Atomic Particles)

Discovery Of Sub-Atomic Particles

For a long time, atoms were considered the smallest, indivisible particles of matter, as proposed by Dalton's atomic theory. However, groundbreaking experiments in the late 19th and early 20th centuries revealed that atoms are actually composed of even smaller particles, called sub-atomic particles. The key discoveries were those of the electron, proton, and neutron.

Discovery Of Electron

The discovery of the electron is credited to J.J. Thomson in 1897, stemming from his investigations into the properties of cathode rays. These rays were observed when a high voltage was applied across electrodes in a partially evacuated glass tube (called a discharge tube or cathode ray tube).

Cathode Ray Tube Experiment: A discharge tube typically consists of a sealed glass tube fitted with two metal electrodes, a cathode (negative electrode) and an anode (positive electrode). When a high voltage (several thousand volts) is applied to the electrodes at very low gas pressures (around $10^{-2}$ to $10^{-3}$ atm, and even lower for observing specific phenomena), a stream of radiation is emitted from the cathode and travels towards the anode. These were termed cathode rays.

Early experiments showed that cathode rays travel in straight lines away from the cathode. J.J. Thomson performed experiments to study the effect of electric and magnetic fields on these rays. His key findings were:

When an electric field was applied perpendicular to the path of the cathode rays, the rays were deflected towards the positive plate of the electric field. This indicated that cathode rays consist of negatively charged particles.
When a magnetic field was applied, the cathode rays were also deflected. The direction of deflection was consistent with the rays being composed of negatively charged particles.
By carefully adjusting the strengths of the electric and magnetic fields such that they cancelled out the deflection of the cathode rays (making the beam hit the fluorescent screen at the original undeflected position), Thomson was able to measure the velocity of the particles and their charge-to-mass ratio.
Most significantly, the properties of the cathode rays (deflection, charge-to-mass ratio) were found to be independent of the material of the cathode and the gas present in the discharge tube. This led Thomson to conclude that these negatively charged particles are fundamental constituents of all atoms.

Thomson named these fundamental negatively charged particles electrons.

Charge To Mass Ratio Of Electron

J.J. Thomson's experiments with cathode rays allowed him to determine the ratio of the electron's electric charge ($e$) to its mass ($m_e$). He used the deflections of the electron beam in combined electric and magnetic fields.

By applying an electric field (E) and a magnetic field (B) perpendicular to each other and to the path of the electron beam, Thomson could measure the deflection. In a purely electric field, the deflection is related to the charge-to-mass ratio and the field strength. In a purely magnetic field, the deflection is also related to the charge-to-mass ratio, the field strength, and the velocity of the particles.

By first using both fields to produce zero net deflection (balancing the electric and magnetic forces, $eE = evB$, allowing calculation of velocity $v = E/B$), and then using only the electric field (or magnetic field) to measure deflection, Thomson was able to calculate the charge-to-mass ratio:

$ \frac{e}{m_e} = \frac{E^2}{2Vy^2 B^2} $ (using electric deflection) or $\frac{e}{m_e} = \frac{v}{rB}$ (using magnetic deflection and radius of curvature $r$)

Where $V$ is the accelerating voltage and $y$ is the deflection observed (simplified forms of equations).

Thomson determined the $e/m_e$ ratio to be approximately $1.759 \times 10^{11}$ C/kg. This value was found to be constant for all cathode rays, regardless of their source.

This extremely large value indicated that either the charge ($e$) is very large or the mass ($m_e$) is very small compared to other particles known at the time.

Charge On The Electron

The exact value of the charge of an electron ($e$) was determined by Robert Millikan through his famous oil drop experiment (1909-1913).

Millikan's Oil Drop Experiment: In this experiment, tiny oil droplets were allowed to fall under gravity between two horizontal charged plates. The droplets were charged by friction as they passed through an atomizer or by using X-rays. By observing the motion of the charged droplets through a microscope and adjusting the electric field between the plates, Millikan could make a droplet suspend in the air (when the electric force balancing the gravitational force). By measuring the charge on many droplets, he found that the charges were always integer multiples of a fundamental value.

Diagram of Millikan's oil drop experiment

The smallest observed charge was found to be the charge of a single electron. Millikan determined the magnitude of the charge of an electron ($e$) to be approximately $1.602 \times 10^{-19}$ C.

The charge of an electron is $-1.602 \times 10^{-19}$ C.

Once the charge of the electron ($e$) was known, its mass ($m_e$) could be calculated using Thomson's experimentally determined charge-to-mass ratio ($e/m_e$):

m_e = \frac{e}{(e/m_e)} = \frac{1.602 \times 10^{-19} \text{ C}}{1.759 \times 10^{11} \text{ C/kg}} \approx 9.109 \times 10^{-31} \text{ kg}

This mass is extremely small, confirming that the electron is a very light particle. This mass is about 1/1837th the mass of a hydrogen atom.

Discovery Of Protons And Neutrons

Discovery of Protons (Anode Rays)

The discovery of the electron, a negatively charged particle, implied that atoms must also contain positive charges to be electrically neutral. The existence of positively charged particles within atoms was demonstrated by E. Goldstein in 1886. He used a modified discharge tube with a perforated cathode.

When voltage was applied at low pressure, in addition to cathode rays moving from cathode to anode, Goldstein observed a new type of rays passing through the holes or canals in the cathode and streaming towards the cathode. These rays were called canal rays or anode rays.

Diagram of a discharge tube showing canal rays

Studies of canal rays showed that they are:

Deflected by electric and magnetic fields in the opposite direction to cathode rays, indicating that they consist of positively charged particles.
The charge-to-mass ratio ($q/m$) of these particles was found to depend on the gas filled in the discharge tube. This suggested that these particles were not universal constituents like electrons but were formed from the ionisation of the gas atoms. When a gas atom loses an electron, it becomes a positively charged ion ($A \to A^+ + e^-$). The canal rays were beams of these positive ions.

The smallest and lightest positively charged particle was obtained when hydrogen gas was used in the discharge tube (since a hydrogen atom has only one proton and one electron). The positive particle from hydrogen gas (H$^+$) was given the name proton by Ernest Rutherford. A proton is a fundamental particle with a positive charge equal in magnitude to the electron's charge ($+1.602 \times 10^{-19}$ C) and a mass approximately equal to that of a hydrogen atom, which is about $1.672 \times 10^{-27}$ kg, roughly 1837 times the mass of an electron.

Discovery of Neutrons

After the discovery of protons, it became clear that the mass of an atom (except for $^{1}$H) was greater than the combined mass of its protons and electrons. For example, Helium has 2 protons (Z=2), but its atomic mass is about 4 times the mass of a proton. This suggested the presence of other particles in the nucleus.

In 1932, James Chadwick performed experiments where he bombarded light elements like beryllium with alpha particles. He observed that a highly penetrating radiation was emitted, which was not deflected by electric or magnetic fields, indicating it was electrically neutral.

Illustration of Chadwick's experiment leading to neutron discovery

By analysing the energy transferred to target particles in collision experiments, Chadwick determined the mass of these neutral particles to be slightly greater than the mass of a proton. He named these particles neutrons.

The neutron is a fundamental sub-atomic particle with no electric charge (neutral) and a mass approximately equal to that of a proton (approx. $1.675 \times 10^{-27}$ kg).

The discovery of the neutron explained the missing mass in atoms and led to the modern understanding of the atomic nucleus containing protons and neutrons.

Thus, the atom is now understood to be composed of three main sub-atomic particles: electrons, protons, and neutrons, with protons and neutrons residing in the dense, central nucleus, and electrons orbiting the nucleus.