Element X on Planet Qatar

Question

Element X on Planet Qatar has three known isotopes: X-121 with a relative abundance of 43.2%, X-123 with a relative abundance of 53.1%, and X-129 with a relative abundance of 3.70%. What is the average atomic mass in amu of Element X given this information? How did Rutherford's experiment change the way scientists had previously viewed atomic structure? How did this pave the way for subsequent changes up to and including the currently accepted quantum mechanical atomic model? How is percent abundance related to average atomic mass?

Answer 1

Hi Tiffany,

We need to find the weighted average of all of these isotopes. The idea of a weighted average just means that isotopes with relatively lower abundance will have less contribution or less "influence" on the average mass than other isotopes with higher abundance. Mathematically, this is:

∑ (isotope abundance * mass of isotope) / Σ (isotope abundance)

we will need to sum this up for all existing isotopes

Notice that Σ (isotope abundance) in the denominator is simply equal to 100, because the sum of all known isotope abundances (expressed in percentages) has to, by definition, equal to 100%.

So this becomes

((121 * 43.2) + (123 * 53.1) + (129 * 3.70)) / 100

This gives you the answer you are looking for.

Now, the other part of your question about atomic theory:

Rutherford's model of the atom, which was elucidated by his "Gold Foil" experiment around 1911, was a revolutionary step in the formulation of modern atomic theory. Most importantly, this experiment provided insight into atomic structure, and Rutherford's model of the atom was proposed as a small, positive, massive nucleus (contains the very vast majority of the mass of the entire atom) with negatively charged electrons surrounding it at relatively large distances. In this way, the volume of an entire atom was understood to be made up primarily of empty space. Historically, this experiment and model were highly significant because only about 10-15 years prior, the electron had been discovered by J.J. Thomson and what we now call the "nucleus" had then only been assumed to be a uniform (non-localized) positive charge that the electrons are embedded in (the so-called "Plum Pudding model" of the atom).

Following Rutherford's model of the atom, the structure of the nucleus became more well-defined with the discovery of protons (1919) and neutrons (1932) as the particle constituents of the nucleus. Meanwhile, physicists and chemists were developing an atomic understanding of chemistry, where each unique element was beginning to be understood as having a unique number of protons in its nucleus. In the physics world, Max Planck and Albert Einstein's foundation of a new theory of matter (and light) (quantum mechanics) was being used to develop mathematical descriptions of atomic systems. Around 1913, Niels Bohr had taken Rutherford's model of the atom and combined it with a bizarre new concept (from quantum mechanics) that the energy of electrons around a nucleus is quantized. Bohr proposed that, in the simplest atom (Hydrogen), the electron orbits the nucleus. Although this model correctly explained some things about the hydrogen atom (namely, its spectral emission), it failed to model the behavior of more complicated atomic systems. It wasn't until the 1920s that a "wave mechanical model" came along through the work of several physicists (most importantly de Broglie, Heisenberg, and Schrodinger) and Bohr's concept of electrons "orbiting" the nucleus was abandoned in favor of "orbitals" which are more abstract probabilistic representations of electronic structure within an atom (quantum mechanics is weird).

Answer 2

Find average mass by M_avg = .432*121+.531*123 + .037*129

The gold foil experiment showed that the atom had a small, very dense + charged nucleus. The hypothesis of a short-range nuclear force was required because all the protons are repelling strongly from each other in the small nucleus.

The percent abundance is related to the number fraction as f_i = P_i/100 and used as in the formula written above in order to find average mass.

Please consider a tutor. Take care.