Question

Why can't helium ions combine with electrons of gold atoms in the Gold foil experiment?

Answer 1

We know that The Rutherford model or the -particle scattering experiment was devised by the New Zealand-born scientist Ernest Rutherford to describe an atom. Understand the use of gold foil in the experiment. With this you can conclude with your observations and thus answer the question.

Complete answer:
The new model for the atom, which was based on experimental results, contained new features of a relatively high central positive charge present in a very small volume in comparison to the complete volume of the atom. This region came to be known as nucleus. Rutherford's gold foil experiment was used to determine the nuclear charge of the respective atom by passing a beam of doubly charged helium ions or rather alpha particles. Gold foil is used for the experiment as it is easy to beat into thin sheets due to high malleability properties
The possibility that helium ions combine with electrons of gold atoms to produce $H{{e}^{+}}$and neutral gold atoms. Presence of such reduced helium particles can be detected now with mass spectrographic instruments. The revolving electron would lose energy.
But the combination can take place only between the gaseous helium ion and ionized electron. The kinetic energy of alpha particles from the radioactive nucleus $Ra226$ and $Ra222$ are $4.86eV$ and $5.59eV$ respectively. Ionization energy of gold atoms is 9.22eV , while the threshold energy of gold metal is $5.447eV$. The alpha particle hence does not have enough energy to release the electron from gold atoms for combination.

Note:
Remember that God foil experiment although proves useful, had its own share of drawbacks. Some are mentioned below: The orbital revolution of the electron is not expected to be stable, Any particle in a circular orbit would undergo an acceleration and the charged particles would radiate energy.