8.3 Nuclear radius

• The nuclear radius constant, denoted as \(r_0\), is approximately 1.2 fm
• Electron diffraction uses the de Broglie wavelength to analyze electron momentum.
• What is a prime example of alpha particle scattering used to determine nuclear radius?

  Rutherford's experiment
• The empirical formula for nuclear radius is \(R = r_0 A^{\frac{1}{3}}\), where \(r_0\) is the nuclear radius constant.
• The nuclear radius is typically measured in fermi, which is equal to 1 × 10⁻¹⁵ meters.
• One fermi is equal to 1 × 10⁻¹⁵ meters.
• The fermi is suitable for the tiny size of the nucleus.
• The nuclear radius depends on the nucleon number.
• Electron diffraction uses the wavelike properties of electrons to map nuclear boundaries.
• Steps in determining nuclear radius using electron diffraction

  1️⃣ Electrons are scattered off nuclei

  2️⃣ Diffraction patterns are produced

  3️⃣ Nuclear size is deduced from the patterns
• How does the scale of nuclear radius compare to atomic radius?

  Nuclear radius is smaller
• What is the composition of the nucleus?

  Protons and neutrons
• Order the following by increasing size: atomic radius, nuclear radius

  1️⃣ Nuclear radius

  2️⃣ Atomic radius
• What is the approximate value of r₀ in the nuclear radius formula?

  1.2 fm
• The atomic radius includes the space occupied by the electron cloud.
• In the nuclear radius formula, what does the term 'r₀' represent?

  Constant
• The nuclear radius is the distance from the center of the nucleus to its boundary
• The nucleon number is also known as the mass number
• Steps in Alpha Particle Scattering:

  1️⃣ Alpha particles are scattered by nuclei

  2️⃣ Scattering angles are analyzed

  3️⃣ Radius estimates are determined
• Match the method with the principle used to determine nuclear radius:

  Electron Diffraction ↔️ Diffraction patterns indicate nuclear size

  Alpha Particle Scattering ↔️ Scattering angles reveal nuclear size
• The nuclear radius constant \(r_0\) is approximately 1.2 fm.


  True
• The fermi unit is preferred over meters because it is more appropriate for the scale of nuclear dimensions.


  True
• Fermi is the preferred unit for expressing nuclear dimensions because it aligns with the typical scale of the nucleus.

  True
• Most stable nuclei have a nuclear radius in the range of 1-10 fm.

  True
• The nuclear radius is a fixed value due to the precise boundaries of the nucleus.

  False
• What principle does alpha particle scattering rely on?

  Coulomb interaction
• The nuclear radius of Carbon-12 is approximately 2.75 fm.
• The Angstrom (Å) is equal to 1 × 10⁻¹⁰ meters.
• The nuclear radius is determined by electron diffraction and alpha particle scattering.
• What does the nucleon number (A) represent?

  Total protons and neutrons
• Experimental methods like electron diffraction and alpha particle scattering are used to determine the nuclear radius.


  True
• The atomic radius is significantly larger than the nuclear radius.


  True
• The nuclear radius can be determined experimentally using electron diffraction and alpha particle scattering.
• The nuclear radius has a fixed value due to the uniform edge of the nucleus.

  False
• Electron diffraction is used to determine nuclear size by analyzing diffraction patterns.


  True
• Alpha particle scattering reveals nuclear size through the analysis of scattering angles.


  True
• What does the nuclear radius depend on according to the empirical formula?

  Nucleon number
• Calculate the radius of a carbon-12 nucleus using the empirical formula, given \(A\) = 12 and \(r_0\) = 1.2 fm.

  2.75 fm
• What is the unit used to measure nuclear radius?

  Fermi (fm)
• How many meters are in one fermi?

  1 × 10⁻¹⁵ m