Nuclear radius (A-level only) Flashcards – AQA A-level Physics (7408)

Why is an alpha particle repelled as it approaches a nucleus?

The alpha particle and nucleus both have positive charge, so they repel electrostatically.

In a head-on alpha-particle approach, what energy conversion occurs by the point of closest approach, assuming negligible nuclear recoil and a sufficiently distant starting point?

The alpha particle’s initial kinetic energy is converted into electrostatic potential energy.

What two assumptions allow the initial kinetic energy of a head-on alpha particle to be equated to its electrostatic potential energy at closest approach?

Nuclear recoil is negligible, and the particle starts sufficiently far from the nucleus.

What equation relates the initial kinetic energy $E_k$ to the closest approach $r$ for an alpha particle of charge $2e$ approaching a nucleus of charge $Ze$?

$E_k = \frac{1}{4\pi\varepsilon_0}\frac{2Ze^2}{r}$

Why does an alpha particle’s distance of closest approach give an estimate of the maximum possible nuclear radius?

The particle turns back due to electrostatic repulsion and need not reach the nuclear surface.

What is the de Broglie wavelength of an electron with momentum $p$?

$\lambda = \frac{h}{p}$

When can electron diffraction provide information about nuclear size?

When the electron wavelength is comparable to nuclear dimensions.

What features appear on a graph of scattered electron intensity against scattering angle for a nucleus?

A central maximum, followed at larger angles by minima and secondary maxima.

What two factors determine the angles of electron diffraction minima for a nucleus?

The electron wavelength and the nuclear size.

How can an electron diffraction pattern be used to determine nuclear radius?

Compare the observed diffraction pattern with the expected pattern.

At a fixed electron wavelength, how does a larger nuclear radius affect the angles of diffraction minima?

The minima occur at smaller angles.

What is the typical order of magnitude of a nuclear radius?

Between $10^{-15}$ and $10^{-14}\,\text{m}$.

How does nuclear radius $R$ depend approximately on nucleon number $A$? Include the approximate constant.

$R = R_0A^{1/3}$, where $R_0 \approx 1.2\times10^{-15}\,\text{m}$.

How does the volume of a spherical nucleus depend on its nucleon number $A$?

$V = \frac{4}{3}\pi R_0^3A$, so volume is proportional to $A$.

How is nuclear mass approximated in terms of nucleon number $A$ and nucleon mass $m_n$?

$A m_n$.

What expression for nuclear density follows from the nuclear radius relationship, in terms of nucleon mass $m_n$ and radius constant $R_0$?

$\rho = \frac{m_n}{\frac{4}{3}\pi R_0^3}$

Why does the observed nuclear radius relationship imply approximately the same density in different nuclei?

Both nuclear mass and volume are proportional to nucleon number, so nucleon number cancels in the density calculation.

What is the approximate density of nuclear material?

$2.3\times10^{17}\,\text{kg m}^{-3}$