8.3 Nuclear radius

• Rutherford's scattering experiment used alpha particles to investigate the structure of atoms
• Observations and implications from Rutherford's scattering experiment

  1️⃣ Most α particles passed straight through

  2️⃣ Atom is mostly empty space

  3️⃣ Some α particles were deflected at small angles

  4️⃣ Positive charge is concentrated in a small region

  5️⃣ A few α particles were deflected backwards

  6️⃣ Nucleus is heavy and positive
• Typical values for the nuclear radius range from 1 to 10 femtometres.


  True
• The constant $r_{0}$ in the empirical formula is approximately 1.2 fm
• Match the parameter with its symbol and value:

  Radius Constant ↔️ $r_{0}$, 1.2 fm

  Nuclear Radius ↔️ $r$, Varies
• What is the constant $r_{0}$ in the empirical formula for nuclear radius called?


  Radius constant
• The value of $r_{0}$ is approximately 1.2 fm.


  True
• What is the nuclear radius related to in terms of the mass number A?

  Proportional to $A^{1 / 3}$
• Heavier nuclei have larger radii compared to lighter nuclei.

  True
• Steps in Rutherford's scattering experiment

  1️⃣ Alpha particles directed at gold foil

  2️⃣ Most particles pass straight through

  3️⃣ Some particles deflected at small angles

  4️⃣ A few particles deflected backwards
• What is the empirical formula for nuclear radius?

  r = r_{0} A^{1 / 3}</latex>
• What is the unit of the radius constant $r_{0}$?


  fm
• What does the mass number $A$ represent in the context of nuclear radius calculations?


  Total protons and neutrons
• The radius constant, $r_{0}$, is approximately 1.2 fm
• What is the empirical formula for calculating the nuclear radius of an atom?

  r = r_{0} A^{1 / 3}</latex>
• The nuclear radius, $r$, is measured in femtometres
• The nuclear radius increases with the mass number of the nucleus.


  True
• The nuclear radius of carbon-12 is approximately 2.4 fm
• How does the nuclear radius change as the mass number increases?

  Increases as the cube root
• What is the nuclear radius of hydrogen-1, which has a mass number of $A =$$1$?


  1.2 fm
• Heavier nuclei have larger radii compared to lighter nuclei.
• Arrange the following isotopes in order of increasing nuclear radius:

  1️⃣ Hydrogen-1

  2️⃣ Carbon-12

  3️⃣ Uranium-238
• What is the nuclear radius of an atom?

  The size of the nucleus
• What was the expected outcome of Rutherford's experiment if Thomson's plum pudding model was correct?

  Alpha particles undeflected
• What is the main difference between the Rutherford model and the plum pudding model?

  Concentrated nucleus
• What is the empirical formula for calculating nuclear radius?

  r = r_{0} A^{1 / 3}</latex>
• How does the nuclear radius change as the mass number increases?

  Increases
• The radius constant $r_{0}$ is fixed at 1.2 fm and does not change.


  True
• The radius constant $r_{0}$ determines the typical size of a nucleus
• Match the parameter with its value:

  Radius Constant ↔️ 1.2 fm

  Nuclear Radius ↔️ Varies
• Typical values for the nuclear radius range from 1 to 10 fm
• What type of particles were used in Rutherford's scattering experiment?

  Alpha particles
• Match the observation in Rutherford's experiment with its implication:

  Most α particles passed straight through ↔️ Atom is mostly empty space

  Some α particles were deflected at small angles ↔️ Positive charge is concentrated

  A few α particles were deflected backwards ↔️ Nucleus is heavy and positive
• The radius constant $r_{0}$ is approximately 1.2 fm.


  True
• To calculate the nuclear radius, plug the mass number into the formula r = 1.2 fm \times A^{1 / 3}</latex>
• What does the mass number of a nucleus represent?

  Total number of protons and neutrons
• Steps to calculate the nuclear radius of a specific element

  1️⃣ Identify the mass number $A$

  2️⃣ Plug the mass number into the formula: $r =$$1.2 fm \times A^{1 / 3}$

  3️⃣ Calculate the result to find the nuclear radius $r$
• What is the nuclear radius of carbon-12, which has a mass number of $A =$$12$?


  2.4 fm
• How is the nuclear radius of carbon-12 calculated using the empirical formula?

  r = 1.2 fm \times 12^{1 / 3}</latex>
• What is the approximate value of the radius constant, $r_{0}$, in femtometres?


  1.2 fm