Size of The Nucleus

The smallest unit of any matter is an atom with the properties of a chemical element and is the basic building block of chemistry. Most of the part inside an atom is empty space with its centre having positively charged particles called protons and neutral particles called neutrons. These protons and neutrons constitute the nucleus of the atom. The nucleus is surrounded by negatively charged particles called electrons which form a cloud around it.

(Image to be added soon)

In this article, we will look into the theory behind the size of the nucleus and see what the Rutherford gold foil experiment proved.

History of Nucleus and Electron

The nucleus is also called “atomic nucleus” and comes from the Latin word “nucleus” which is another word for “nux” (it means kernel or nut). Michael Faraday coined this term in 1844 when he was trying to describe the centre of an atom. The sciences which study the composition and characteristics of a nucleus are called nuclear physics and nuclear chemistry.  

• J.J.Thompson carried out his cathode ray tubes experiment and found out that all atoms contain negatively charged particles called electrons.

• In the “Plum pudding model” given by Thompson, an atom had negatively charged electrons meshed inside a positively charged “soup.”

• Rutherford gold foil experiment discovered that most parts of an atom are empty and its centre has a positively charged nucleus.

Facts about Nucleus

• There is a strong electric force between protons and neutrons within the nucleus which holds them together.

• Electrons are attracted towards the nucleus due to the positive proton in it, but they are moving so fast that they either fall around it or orbit it at a distance.

• The positive charge of the nucleus comes from protons in it.

• Protons and neutrons weigh much more than the tiny electrons; hence almost all the mass of a nucleus is centred around the nucleus.

• The proton count of a nucleus determines it as an atom of a specific element.

• The neutron count of a nucleus determines which isotope of an element is that atom.

Rutherford Gold Foil Experiment

J.J. Thompson had proposed the model of an atom, but it was Ernest Rutherford’s model that was finally accepted as the correct nuclear model. The final model was given after the Rutherford Gold Foil Experiment. Rutherford wanted to know how electrons were arranged within an atom. To do this, he decided to carry out an experiment and made fast-moving particles (alpha particles ɑ) fall on a thin gold foil. 

• Alpha particles are helium ions (doubly charged) with a mass of 4μ and possess a considerable amount of energy.

• The gold foil was selected since he needed an extremely thin layer. The thickness of this gold foil was around that of 1000 atoms. 

• ɑ particles are much heavier compared to protons; hence he was expecting them to deflect only slightly by the gold atoms’ subatomic particles.

But he got very unexpected results from this experiment.

(Image to be added soon)

As Per His Observations

• A larger chunk of fast-moving alpha particles passed straight through the gold foil without any deflection.

• There were deflections of small angles for some of the alpha particles.

• The most surprising discovery was the complete rebound of a few alpha particles. At least 1 out of every 12,000 particles rebounded.

What Rutherford Concluded From This Experiment

• Since most ɑ particles passed through the gold foil, most of the atom is an empty space.

• Since the number of particles that got slightly deflected was very few, it was concluded that the charge of the atom occupied a tiny space.

• Since there was a complete bouncing off of a few particles from the gold foil, the atom of the gold foil's positive charge was concentrated in a small volume within the atom.

Rutherford Proposed The Following Nuclear Model of An Atom Based on His Experiment

• The centre of an atom is positively charged, and almost all of an atom’s mass is contained in the central part called the nucleus.

• Electrons have well-defined orbits around the nucleus.

• The size of atomic nucleus is quite small in comparison to the atom’s size.

What is the Size of Nucleus?

A nucleus size is much smaller than the atom’s size. The size of a hydrogen atom is 145,000 times its nucleus. The hydrogen nucleus is the smallest (1.75 * 10-15 m) since it has a single proton.  The size of nucleus is of the order of 1.2 * 10-15 m, and the nuclear radii range from 1 - 10 * 10-15 m. Some nucleus is spherical while some are flattened and have deformed shapes. The formula to measure the size of nucleus is:

R = R0A1/3

Where R0 = 1.2 * 10-15 m

Density of Nuclear Matter

The density of a nucleus (ρ) is its mass divided by the total volume. The number of protons and neutrons are called nucleons, and the mass of a nucleus is A time the mass of the nucleon (A is the number of nucleons in the atom).

mnucleon ~ ⅙ * 10-27 kg

Volume = 4/3 * π * R3, Here R = R0A1/3

Density of nuclear matter ρ = mnucleon/Volume ~ 2 * 1017 kg/m3