Nuclear Size and Density Quiz

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the approximate size of the gold nucleus?

  • $10^{-14}$ m (correct)
  • $10^{-18}$ m
  • $10^{-22}$ m
  • $10^{-10}$ m

Which of the following factors influences the scattering angle of an alpha particle interacting with a gold nucleus?

  • The mass of the alpha particle
  • The kinetic energy of the alpha particle
  • The charge of the gold nucleus
  • All of the above (correct)

Why is the probability of a close collision between an alpha particle and a gold nucleus low?

  • Alpha particles are repelled by the electron cloud.
  • The gold nucleus has a very large mass.
  • The nucleus occupies a very small volume. (correct)
  • The alpha particle has a very small mass.

What does the principle of energy conservation tell us about the distance of closest approach (d) between an alpha particle and a gold nucleus?

<p>The alpha particle's kinetic energy is converted into potential energy at d. (B)</p> Signup and view all the answers

What is the significance of the alpha particle's kinetic energy being 1.2 x 10^-12 J in the calculation of the distance of closest approach?

<p>It represents the initial kinetic energy of the alpha particle before it interacts with the gold nucleus. (C)</p> Signup and view all the answers

Which of the following represents the charge of the gold nucleus, as used in the provided equation for the distance of closest approach?

<p>79e (B)</p> Signup and view all the answers

What is the relationship between the distance of closest approach (d) and the kinetic energy of the alpha particle?

<p>d is inversely proportional to the kinetic energy. (A)</p> Signup and view all the answers

What is the main reason why more energetic alpha particles were able to get closer to the nucleus than expected?

<p>They have higher momentum, allowing them to overcome the electrostatic repulsion. (B)</p> Signup and view all the answers

Why is Coulomb's law used to model the scattering of alpha particles from gold nuclei?

<p>Coulomb's law describes the electrostatic force, which is the dominant force governing the interaction between charged particles like alpha particles and gold nuclei. (A)</p> Signup and view all the answers

In Rutherford's alpha-scattering experiment, what percentage of alpha particles were deflected at angles greater than 90°?

<p>0.01% (B)</p> Signup and view all the answers

If the alpha particles in Rutherford's experiment were replaced with beta particles, which of the following would be the most likely outcome?

<p>A significant decrease in the number of beta particles deflected at greater than 90° angles. (B)</p> Signup and view all the answers

The alpha-scattering experiment provided evidence for which of the following concepts related to atomic structure?

<p>The existence of a nucleus and its relative size compared to the atom. (B)</p> Signup and view all the answers

Which of these is NOT a conclusion drawn from Rutherford's alpha-scattering experiment?

<p>The electrons are arranged in energy levels within the atom. (C)</p> Signup and view all the answers

Imagine a similar experiment where alpha particles are fired at a very thin sheet of a different element, such as aluminum. Compared to the alpha particles scattering from gold foil, what would you expect to see?

<p>Fewer alpha particles scattered at large angles due to the smaller atomic number of aluminum. (C)</p> Signup and view all the answers

Which of the following statements accurately describes the relationship between the alpha-scattering experiment and Thomson's plum pudding model?

<p>Rutherford's experiment debunked Thomson's model completely. (C)</p> Signup and view all the answers

If instead of a gold foil, a thin sheet of a much heavier element like uranium was used in the alpha-scattering experiment, what would be the most likely outcome?

<p>More alpha particles would be scattered at large angles. (C)</p> Signup and view all the answers

If the alpha particles used in the experiment were replaced with protons, what would be the most significant change to the experiment?

<p>Protons would be more likely to be deflected at large angles due to their positive charge. (C)</p> Signup and view all the answers

Using the information from the experiment, how could you estimate the relative size of the nucleus compared to the atom?

<p>By analyzing the percentage of particles not deflected, you can estimate the ratio of the volume of the atom to the volume of the nucleus. (A)</p> Signup and view all the answers

If the radius of a nucleus is doubled, what happens to the density of the nucleus?

<p>The density remains the same. (A)</p> Signup and view all the answers

A hypothetical atom has a nucleus with a radius of 3.6 fm. The nucleus is composed of 20 protons and 20 neutrons. What is the approximate density of the nucleus? (1 fm = 10^-15 m, 1 u = 1.661 x 10^-27 kg)

<p>2.3 x 10^17 kg m^-3 (A)</p> Signup and view all the answers

A nucleus with a nucleon number of 64 has a radius of approximately:

<p>4.8 fm (A)</p> Signup and view all the answers

A hypothetical atom's nucleus has a radius of 2.4 fm. What is the approximate nucleon number of this nucleus? (1 fm = 10^-15 m, 1 u = 1.661 x 10^-27 kg)

<p>8 (B)</p> Signup and view all the answers

Which of the following statements about the strong nuclear force is NOT true?

<p>The strong nuclear force is much weaker than the electrostatic force between protons. (C)</p> Signup and view all the answers

Imagine that a hypothetical nucleus composed of only protons is discovered. Which of the following statements best describes why such a nucleus is extremely unlikely to exist?

<p>The strong nuclear force would be too weak to overcome the electrostatic repulsion between the protons. (B)</p> Signup and view all the answers

The density of a nucleus is primarily determined by:

<p>The mass of the nucleus. (D)</p> Signup and view all the answers

Flashcards

Alpha-Particle Scattering Experiment

An experiment demonstrating the atomic structure through alpha particles interacting with gold foil.

Nuclear Model of the Atom

A model proposing that atoms consist of a small, dense nucleus surrounded by empty space.

Plum Pudding Model

J.J. Thomson's model suggesting atoms are a mix of positive and negative charges.

Observations from the Experiment

Most alpha particles passed through foil, while few were deflected, indicating atomic structure.

Signup and view all the flashcards

Alpha Particles

Positively charged particles emitted from a radioactive source, used in scattering experiments.

Signup and view all the flashcards

Gold Foil

Thin sheet used in the alpha-particle scattering experiment to study atomic structure.

Signup and view all the flashcards

Deflection of Alpha Particles

Change in direction of alpha particles when they encounter the nucleus of an atom.

Signup and view all the flashcards

Empty Space in Atoms

The majority of an atom's volume is empty space, according to scattering results.

Signup and view all the flashcards

Nucleus

Dense, positively charged center of the atom containing most of its mass.

Signup and view all the flashcards

Nucleon number

The total number of protons and neutrons in a nucleus.

Signup and view all the flashcards

Nucleus size equation

R = r0A^(1/3), where R is the nucleus radius and r0 is approximately 1.2 fm.

Signup and view all the flashcards

Nuclear density

The density of atomic nuclei, approximately 10^17 kg/m^3.

Signup and view all the flashcards

Helium-4 nucleus density calculation

Density of a helium-4 nucleus is approximately 2.3 x 10^17 kg/m^3.

Signup and view all the flashcards

Repulsive electrostatic force

The force between protons due to their positive charges, calculated using Coulomb's law.

Signup and view all the flashcards

Strong nuclear force

A powerful force that holds protons and neutrons together in the nucleus, overcoming electrostatic repulsion.

Signup and view all the flashcards

Volume of a nucleus

The volume is V = (4/3)π(r0A^(1/3))^3.

Signup and view all the flashcards

Scattering angle

The angle at which a particle deviates from its original path after collision.

Signup and view all the flashcards

Head-on collision

A direct impact where one particle collides straight with another.

Signup and view all the flashcards

Coulomb's law

A formula that describes the force between two charged particles.

Signup and view all the flashcards

Radius of the gold nucleus

The estimated size of the gold nucleus, about $10^{-14}$ m.

Signup and view all the flashcards

Distance of closest approach (d)

The minimum distance between the alpha particle and the nucleus during collision.

Signup and view all the flashcards

Kinetic energy of alpha particles

The energy an alpha particle has due to its motion, here measured as 1.2 x 10^-12 J.

Signup and view all the flashcards

Gold nucleus charge

The total charge of the gold nucleus, calculated as +Ze, where Z = 79.

Signup and view all the flashcards

Alpha particle charge

The charge of an alpha particle, which is +2e.

Signup and view all the flashcards

Study Notes

Nuclear size and density

  • The radius of the nucleus depends on the nucleon number A of the nucleus.
  • Fast-moving electrons have de Broglie wavelengths of about 10⁻¹⁵ m.
  • Diffraction of such electrons has been used to determine the radii of nuclei.
  • The radius is given by the equation: R = r₀A¹/³
  • Where r₀ has an approximate value of 1.2 fm (1 fm = 10⁻¹⁵ m).
  • The simplest nucleus is that of hydrogen - ¹H, with A = 1.
  • Therefore, think of r₀ as roughly the radius of a proton.
  • The nucleus of an atom is very small but massive (10¹⁷ kg⁻³).
  • All nuclei have a density of around 10¹⁴ kg m⁻³.
  • A spoonful of nuclear material would have a mass of about a thousand million tonnes.
  • Ordinary matter, made of atoms and not just nuclei, has a density of around 10³ kg m⁻³.

Worked example: Density of a helium nucleus

  • Step 1: Calculate the volume of the helium-4 nucleus
    • volume of nucleus = ⁴⁄₃πr₀³A = ⁴⁄₃π(1.2 x 10⁻¹⁵)³ x 4 = 2.895... x 10⁻⁴⁴ m³
  • Step 2: The approximate mass of the helium-4 nucleus is 4 u.
    • density = mass/volume = (4 x 1.661 x 10⁻²⁷) / (2.895... x 10⁻⁴⁴) = 2.3 x 10¹⁷ kg m⁻³
  • Step 3: The mass of the electrons in a helium atom is negligible, so the mass of the helium-4 atom is about 4 u.
    • density of atom = (4 x 1.661 x 10⁻²⁷)/ (⁴⁄₃π x (10⁻¹⁰)³) = 1600 kg m⁻³

Nature of the strong nuclear force

  • In a helium-4 nucleus, the two protons are separated by a distance of about 10⁻¹⁵ m and exert a large repulsive force on each other.
  • According to Coulomb's law, the repulsive electrostatic force F is given by:
    • F = Q₁Q₂ / 4πε₀r² = [(1.60 x 10⁻¹⁹)²] / [4π x 8.85 x 10⁻¹² x (10⁻¹⁵)²] = 230 N
  • This is an extremely large repulsive force, so why do the protons not fly apart?
  • The attractive gravitational force between the protons is far too small (about 10⁻³⁴ N).
  • There must be another, much stronger force acting on the protons. This force is the strong nuclear force.
  • Figure 3 shows a graph of how the nuclear force F varies with separation r for two nucleons.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

More Like This

Atomic and Nuclear Structure Quiz
15 questions

Atomic and Nuclear Structure Quiz

BeneficiaryWhite avatar
BeneficiaryWhite
Basic Nuclear Physics: Atomic Structure
32 questions

Basic Nuclear Physics: Atomic Structure

ExcellentBougainvillea3017 avatar
ExcellentBougainvillea3017
Basic Nuclear Physics - Atomic Structure
32 questions

Basic Nuclear Physics - Atomic Structure

PoisedArgon avatar
PoisedArgon
Atomic Structure and Nuclear Physics
491 questions

Atomic Structure and Nuclear Physics

WellManneredRadium4817 avatar
WellManneredRadium4817
Use Quizgecko on...
Browser
Open
Browser
Browser