Identify the statements that are correct based only on Rutherford's nuclear theory as it was originally stated

i. Neutral helium atoms contain more electrons than protons.

ii. The atom's volume is mostly empty space. 

iii. The nucleus of an atom composes most of the volume of an atom.

iv. Neutral helium atoms contain more protons than neutrons.

The approximate diameter of a gold atom is 270 pm and its nucleus has a diameter of 1.0 x 10^–2 pm. Calculate the fraction of the α particles in Rutherford's gold foil experiment that are scattered at large angles by using the cross-sectional area occupied by the nucleus as a fraction of that occupied by the atom. Assume a gold foil that is 4 layers thick with the nuclei equally offset from each other such that no crosssection overlaps.

There are two different isotopes of chlorine and these are ³⁵Cl (abundance = 75.78 %) and ³⁷Cl (abundance = 24.22 %). Under a certain condition, a mass spectrum of Cl₂ consists of three peaks (Peak 1 - 69.938 u, Peak 2 - 71.935 u, and Peak 3 - 73.932 u) with a relative abundance ratio of 9:6:1. Determine which two atoms comprising a Cl₂ molecule gave each peak. 

Nitrogen has two stable isotopes: Nitrogen-14 and nitrogen-15. If a sample of nitrogen gas (N2) is analyzed using mass spectrometry, the following peaks (relative height in parenthesis) are obtained: m/z 28 (100 %); m/z 29 (0.731 %); m/z 30 (0.001 %). Using this data, calculate the abundance of each isotope.

Mass spectrometry can reveal the presence of isotopes of an element in a compound being analyzed. Isotopes, as separate peaks, can most easily be seen next to the molecular ion peak. Chlorine has two isotopes: Chlorine-35 (abundance 76 %) and chlorine-37 (abundance 24 %). If chloromethane (CH₃Cl) is subjected to mass spectrometry, how many molecular ion peaks will the mass spectrum have?

The mass spectrum for the stable isotopes of iron (⁵⁴Fe, ⁵⁶Fe, ⁵⁷Fe, and ⁵⁸Fe) is shown below.

Calculate the average atomic mass of iron using the data above and compare it with the periodic table value.

Which among the following subatomic particles (electron, proton, or neutron) was the most difficult to discover? Why?