The quantum model and subatomic particles

In the current quantum model, we no longer speak of orbits, as Bohr did, but of orbitals. Explain the difference between an orbit and an orbital: what information does each provide about the electron, and which of the two concepts describes a definite trajectory?

The principal quantum number $n$ labels the energy levels of the atom.

1. a) What values can $n$ take?
2. b) What happens to the energy of the level and the average size of the electron cloud when $n$ increases?

Within each energy level, there are subshells. In this topic, we will study the s and p subshells: the s orbital is spherical, and each p orbital is shaped like two symmetrical lobes. Their shapes are shown in the figure.

1. a) What is the maximum number of electrons that can fit in an s orbital?
2. b) A p subshell has $3$ orbitals: how many electrons in total can fit in a p subshell?

Electrons occupy the subshells in this order: $1s$, $2s$, $2p$, $3s$, $3p$. Each s subshell can hold $2$ electrons and each p subshell, $6$.

1. a) Write the electron configuration of sodium ($Z = 11$) and of chlorine ($Z = 17$).
2. b) How many electrons does each of the two atoms have in its outer occupied shell?

In $1927$, Heisenberg stated his uncertainty principle. Explain what this principle states about the position and velocity of the electron, and why, because of it, physicists depict the electron as a "probability cloud" rather than a small ball following a trajectory.

Iodine is an essential trace element added to table salt; its most common isotope has $Z = 53$ and $A = 127$.

1. a) Calculate the number of protons, neutrons and electrons in a neutral iodine atom.
2. b) Write its symbol using the notation ${}^{A}_{Z}\text{X}$.

The average atomic mass of boron is $10,8\ \text{u}$ and its two natural isotopes are boron-10 and boron-11.

1. a) Call $x$ the fraction of boron-10 and set up the equation satisfied by the weighted average: $10\cdot x + 11\cdot(1 - x) = 10,8$.
2. b) Solve it and express the abundances of each isotope as percentages.
3. c) Check the result by calculating the average mass again using these abundances.

Tooth enamel contains calcium and many toothpastes contain fluorine.

1. a) The calcium atom ($Z = 20$) forms the $\text{Ca}^{2+}$ ion: how many electrons does this ion have?
2. b) The fluorine atom ($Z = 9$) forms the $\text{F}^{-}$ ion: how many electrons does this ion have?
3. c) Explain, considering their electron configurations, why atoms tend to gain or lose electrons until they achieve a full outer shell.

In cancer radiotherapy, cobalt-60 is used as a radioactive source with $Z = 27$.

1. a) Write the symbol for cobalt-60 using the notation ${}^{A}_{Z}\text{X}$.
2. b) Calculate its protons, neutrons and electrons, assuming a neutral atom.
3. c) What is the difference between cobalt-60 and cobalt-59, the stable isotope of the same element?

Naturally occurring magnesium has three isotopes: magnesium-24 ($78,7\ \%$), magnesium-25 ($10,1\ \%$) and magnesium-26 ($11,2\ \%$).

1. a) Calculate the average atomic mass of magnesium as a weighted average.
2. b) Explain why the result is much closer to $24$ than to $26$.
3. c) Could the average mass of an element be equal to an integer? Explain in which case this would occur.

Consider these three species: $\text{F}^{-}$ ($Z = 9$), $\text{Ne}$ ($Z = 10$) and $\text{Na}^{+}$ ($Z = 11$).

1. a) Calculate the number of electrons of each one.
2. b) Are they the same element? Are they isotopes of each other? Justify both answers.
3. c) Write the common electron configuration of all three species in the order $1s$, $2s$, $2p$ and explain why they are said to be isoelectronic.