Nuclear radius and density

Information about the radius of a nucleus can be deduced from the closest approach of alpha particles and from electron diffraction.

Alpha particles, each with a kinetic energy of 5.59 MeV, are fired at a thin foil made of

Some of the alpha particles are scattered through an angle of 180°.

Estimate the radius of a 197 79Au nucleus from this information.

Explain why your answer to Question 01.1 is an estimate.

Electron diffraction gives a more precise value for the radius of the nucleus.

Sketch, on Figure 1, a graph of intensity against angle for electron diffraction by a nucleus. Go on to state the feature of this graph that is used to determine the radius of the nucleus.

Results from electron-diffraction experiments lead to the equation:

Show that the equation provides evidence for the constant density of nuclear material.

The nuclear radius of an element with nucleon number x is r.

What is the nuclear radius of an element with nucleon number y ?

What can be deduced about the radius r of a nucleus of gold from the scattering of alpha particles by gold nuclei?

Nuclear radii can be estimated using either alpha particles or high-energy electrons.

State two advantages of using high-energy electrons rather than alpha particles for this estimate.

Figure 11 shows a beam of electrons, each with the same high energy, incident on a target gas. The electrons are diffracted by the nuclei in the gas. The intensities of these diffracted electrons are measured at various angles θ. The data are used to determine the nuclear radius R of the atoms in the gas.

Sketch on Figure 12 a graph showing how the electron intensity varies with θ.

Show that this equation is consistent with the idea that all nuclei have the same density.

Suggest one reason why the constant density of nuclear material derived from this equation is only approximate.

Calculate an estimate of

• the constant R₀

• the density of nuclear material.

An alpha particle is moving towards a stationary gold nucleus. The alpha particle has a kinetic energy of 9.0 × 10⁻¹³ J when it is a large distance from the gold nucleus. The gold nucleus contains 79 protons.

What is the closest possible distance of approach of the alpha particle to the gold nucleus?

Figure 11 shows alpha particles all travelling in the same direction at the same speed. The alpha particles are scattered by a gold (¹⁹⁷₇₉Au) nucleus. The path of alpha particle 1 is shown.

State the fundamental force involved when alpha particle 1 is scattered by the nucleus in Figure 11.

Draw an arrow at position X on Figure 11 to show the direction of the rate of change in momentum of alpha particle 1

Suggest one of the alpha particles in Figure 11 which may be deflected downwards with a scattering angle of 90°

Justify your answer.

Alpha particle 4 comes to rest at a distance of 5.5 × 10⁻¹⁴ m from the centre of the

Calculate the speed of alpha particle 4 when it is at a large distance from the nucleus. Ignore relativistic effects.

mass of alpha particle = 6.8 × 10⁻²⁷ kg

The nuclear radius of¹⁹⁷₇₉Au is 6.98 × 10⁻¹⁵ m.

Calculate the nuclear radius of¹⁰⁷₄₇Ag.

All nuclei have approximately the same density.

State one conclusion about the nucleons in a nucleus that can be deduced from this fact.

nucleus?

The radius of a uranium²³⁸₉₂U nucleus is 7.75 × 10¹⁵ m What is the radius of a¹²₆C nucleus?

What is the radius of a nucleus of the uranium nuclide²³⁸₉₂U?