Size of the Nucleus: Rutherford Gold Foil Experiment

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Jasmine Grover

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Rutherford Atom Model was the first proper and correct interpretation of the atom, and it served as the foundation for Bohr's interpretation. Physics essentially requires an understanding of the underlying structure of matter. An atom is the smallest unit of matter and the basic building block of chemistry. The majority of an atom's interior is empty space, with protons (positively charged particles) and neutrons (neutral particles) in the centre. The nucleus of the atom is made up of protons and neutrons. It would have been impossible to determine the size of the nucleus without the Rutherford gold foil experiment,

Key Takeaways: Nucleus, Gold Foil Experiment, Atom, Plum Pudding Model, Nuclear Density, Neutron, Proton, Electron, Rutherford Atom Model, Elements


Nucleus and Electron Evolution

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The term "atomic nucleus" is derived from the Latin word "nucleus," which is another word for "nux" (it means kernel or nut). When Michael Faraday was seeking to define the centre of an atom in 1844, he developed this word. Nuclear physics and nuclear chemistry are the sciences that examine the composition and properties of nuclei.

  • J.J. Thompson used cathode ray tubes to discover that all atoms contain negatively charged particles known as electrons.
  • Thompson's "Plum pudding model" depicted an atom with negatively charged electrons mingling with a positively charged "soup."
  • The Rutherford gold foil experiment revealed that most of an atom's components are empty, and its nucleus is positively charged.

Nuclei Class 12 Important Notes PDF

Nuclei Class 12 Important Notes

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Facts about Nucleus

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Some important facts about the nucleus are stated below:

  • Within the nucleus, there is a strong electric force that holds protons and neutrons together.
  • The positive proton in the nucleus attracts electrons, but they are flying so quickly that they either fall around it or orbit it at a great distance.
  • The protons in the nucleus provide it with a positive charge.
  • Because protons and neutrons are substantially heavier than electrons, practically all of a nucleus' mass is concentrated around the nucleus.
  • A nucleus' proton count identifies it as an atom of a given element.
  • The number of neutrons in a nucleus defines the isotope of the element an atom belongs to.

Rutherford’s Gold Foil Experiment

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The Thomson or "plum pudding" model of the atom was the best model that was present before the experiment of Rutherford. The atom, according to this idea, is made up of a positive substance "pudding" with negative "plums" strewn around. Rutherford's alpha-particle scattering experiment later revolutionised our understanding of atomic structure. To test this idea, Rutherford fired alpha particle beams at thin gold foil and observed how the alpha particles scattered.

JJ Thomson's Plum Pudding Model

JJ Thomson's Plum Pudding Model

Rutherford demonstrated that the atom was mostly empty space, with the nucleus at the centre and electrons circulating around it, in his experiment. When alpha particles were fired onto gold foil, Rutherford noted that one out of every 20000 particles changed orientation by more than 90 degrees. The leftover 19999 particles strayed a few millimetres from their intended path. This led to the conclusion that the atom was mostly empty space with the majority of the mass concentrated in tiny volumes at the centre. This central volume was called 'the nucleus,' which is Latin for 'small nut.'

Rutherford’s Gold Foil Experiment

Rutherford’s Gold Foil Experiment

Rutherford made three observations as a result of this experiment:

  • Some alpha particles were redirected at extreme angles.
  • Only a few alpha particles were deflected backwards in this experiment.
  • Highly charged alpha particles passed through the foil without being deflected. If the plum pudding model was right, this would have been the expected result for all of the particles.

What Rutherford Discovered as a Result of His Experiment?

  • Because the majority of particles travel through the gold foil, the atom is mostly empty space.
  • Because the number of particles slightly deflected was so little, it was determined that the atom's charge occupied a very small space.
  • The positive charge of the gold foil atom was concentrated in a limited volume within the atom due to the total bouncing off of a few particles from the gold foil.

Nuclear Model of an Atom: Rutherford’s Proposal

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On the basis of his experiment, Rutherford proposed the following nuclear model of an atom:

  • The nucleus, the centre component of an atom, is positively charged and contains approximately all of the mass of the atom.
  • The orbits of electrons around the nucleus are well-defined.
  • In relation to the size of the atom, the atomic nucleus is quite small.

Size of the Nucleus

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The size of the nucleus was allowed to be determined under Rutherford’s experiment. By obtaining the point of closest approach of an alpha particle, we may compute the size of the nucleus. The point of closest approach was determined to be around 4×10-14m by launching alpha particles with a kinetic energy of 5.5 MeV. There is no touch since the repelling force is Coulomb repulsion. This indicates that the nucleus is smaller than 4×10-14m in size.

After many more iterations of the experiment, the diameters of the nuclei of various elements were correctly measured. After then, a formula for calculating the nucleus' size was devised.

R = R0 A1/3

where R0 = 1.2 * 10-15 m

We can deduce from the formula that the nucleus' volume, which is proportional to R3, is proportional to A. (mass number). Another thing to notice about the equation is that there is no mention of density in it. The reason for this is that the density of nuclei does not change with the elements. The nucleus has a density of approximately 2.3 × 1017 kg.m-3.

The video below explains this:

Nuclear Size Detailed Video Explanation:


Things to Remember

  • Rutherford's "gold foil experiment" led to the finding that the nucleus, or dense area, contains the majority of an atom's mass.
  • Rutherford's gold foil experiment provided evidence that the plum pudding model of the atom was inaccurate.
  • The formula for measuring the size of the nucleus was developed based on Rutherford's gold foil experiment id given as R= R0A1/3.
  • The mass of a nucleus is divided by the total volume to determine its density (ρ). Nucleons are the number of protons and neutrons in a nucleus, and their mass is A times the mass of the nucleon (A is the number of nucleons in the atom).
  • In 1913, physicist Niels Bohr refined Rutherford's finding of the nucleus and postulated atomic structure.

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Sample Questions

Ques. What was the purpose of Rutherford's experiment, and what did he learn? (3 Marks)

Ans. To study the structure of the atom, the Rutherford gold foil experiment was utilised. Rutherford and his students shot positively charged alpha particles through cold foil surrounded by a tube with a phosphorescent screen to see where they landed. The pre-Rutherford atomic model predicted that the alpha particles would almost entirely pass straight through the foil, however, the data revealed that the alpha particles were also scattered by the foil. According to Rutherford's findings, atoms must have a big positively charged nucleus at their centre, and they are essentially empty spaces.

Ques. What happened in Rutherford's experiment? (3 Marks)

Ans. The Rutherford Gold Foil experiment used minute particles to fire at a thin covering of gold. A tiny percentage of the particles were observed to be deflected, while the rest passed through the layer. As a result, Rutherford deduced that an atom's mass was concentrated at its centre.

Ques. What was the outcome of the gold foil experiment? (3 Marks)

Ans. The Rutherford gold foil experiment involved firing positively charged alpha particles through gold foil and then watching where they landed. Rutherford and his students made their observations using phosphorescent screens, which emitted light when touched by alpha particles. Under a microscope, the alpha particles would produce scintillation markings on the screen, which could be seen.

Ques. In Rutherford's gold-foil experiment, what caused the alpha particles to deflect? (2 Marks)

Ans. The particles, according to Rutherford, would travel directly through the foil. However, he discovered that as the particle passed through the foil, its course was changed or deflected. This is because like charges repel each other.

Ques. What impact did Rutherford's experiment have on the world? (3 Marks)

Ans. Rutherford's experiment improved our understanding of matter and made it more practical. The experiment disproved earlier theories about matter and established a new model that was consistent with the data.

Ques. What is the purpose of using gold foil in the Rutherford experiment? (3 Marks)

Ans. In Rutherford's ray scattering experiment, the gold foil is utilised because of its increased malleability. Incredibly thin gold foil is utilised in the experiment, and gold may be moulded into very thin sheets.

Ques. What was the outcome of the gold foil experiment? (3 Marks)

Ans. The Rutherford gold foil experiment involved firing positively charged alpha particles through gold foil and then watching where they landed. Rutherford and his students made their observations using phosphorescent screens, which emitted light when touched by alpha particles. Under a microscope, the alpha particles would produce scintillation markings on the screen, which could be seen.

Ques. Explain the term "isotopes of an element" with an example. (5 Marks)

Ans. Isotopes are formed when two atoms of the same element have the same number of protons but differ in numerous neutrons. The quantity of neutrons in various isotopes differs, resulting in differing atomic masses. The superscript 2 on the left side of the element shows the sum of protons and electrons in the isotope, and the isotope is written as 2H.

In nature, carbon has three isotopes: Carbon-12, Carbon-13, and Carbon-14, for example. These isotopes all have six protons, but they have different numbers of neutrons: 6, 7, and 8. Chemically, isotopes are not differentiated because they all contain the same amount of electrons. Despite the fact that all isotopes are identical, some can transition into a different element.

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CBSE CLASS XII Related Questions

  • 1.
    Two small identical metallic balls having charges \( q \) and \( -2q \) are kept far at a separation \( r \). They are brought in contact and then separated at distance \( \frac{r}{2} \). Compared to the initial force \( F \), they will now:

      • attract with a force \( \frac{F}{2} \)
      • repel with a force \( \frac{F}{2} \)
      • repel with a force \( F \)
      • attract with a force \( F \)

    • 2.
      Draw the number of scattered particles versus the scattering angle graph for scattering of alpha particles by a thin foil. Write two important conclusions that can be drawn from this plot.


        • 3.
          Two parallel plate capacitors X and Y are connected in series to a 6 V battery. They have the same plate area and same plate separation but capacitor X has air between its plates, whereas capacitor Y contains a material of dielectric constant 4. Calculate the capacitances of X and Y, if the equivalent capacitance of the combination of X and Y is \( 4 \, \mu\text{F} \). Calculate the potential difference across the plates of X and Y.


            • 4.
              Write any two features of nuclear forces.


                • 5.
                  What is displacement current (\( i_d \))? Considering the case of charging of a capacitor, show that \( i_d = \varepsilon_0 \frac{d\Phi_E}{dt} \). What is the value of \( i_d \) for a conductor across which a constant voltage is applied?


                    • 6.
                      A tank is filled with a liquid to a height of \( 12.5 \, \text{m} \). The apparent depth of a needle lying at the bottom of the tank is measured to be \( 9.0 \, \text{m} \). Calculate the speed of light in the liquid.

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