# Atomic structure and quantized description

Physics I · Chemistry · https://tryals.app/learn/physics-i/atomic-structure-and-quantized-description

## Atomic Structure & Numbers

Matter is built from **atoms**, featuring a dense **nucleus** of protons and neutrons surrounded by electrons in quantized energy levels. An electron's state is defined by four **quantum numbers**.

| Number | Name | Allowed Values | Description |
| --- | --- | --- | --- |
| $n$ | **Principal** | $1, 2, 3, \ldots$ | Shell size & energy |
| $\ell$ | **Angular** | $0$ to $n-1$ | Subshell shape ($s, p, d, f$) |
| $m_\ell$ | **Magnetic** | $-\ell$ to $+\ell$ | Orbital orientation |
| $m_s$ | **Spin** | $+\tfrac{1}{2}, -\tfrac{1}{2}$ | Intrinsic electron spin |

**Electron configuration** rules govern how these states fill:

* **Aufbau principle**: Fill lowest energy orbitals first.
* **Pauli exclusion**: No two electrons share all four quantum numbers.
* **Hund's rule**: Maximize unpaired spins within a subshell.

## Models & Stoichiometry

In the **Bohr model**, electrons inhabit fixed paths with quantized angular momentum $L = n\hbar$ ($n = 1, 2, \ldots$). Transitions emit or absorb photons where $\Delta E = E_f - E_i$.

**Key Relationships**

* **Amount of substance**: $n = m/M$ ($m$ = mass, $M$ = molar mass).
* **Avogadro's number**: $N_A = 6.022\times 10^{23}\;\text{mol}^{-1}$.
* **Ideal gas law**: $PV = nRT$.
* **Hydrogen energy**: $E_n = -13.6/n^{2}\;\text{eV}$ (from the **Schrödinger equation**).

> **Common pitfall**: Electron orbits are a cartoon. Orbitals are probability clouds, and transitions are instantaneous quantum jumps, not gradual spirals.

## Practice questions

5 of this lesson's 11 practice questions, with answers. The full set is in the app.

### 1. The atomic number of an element equals the number of protons in its nucleus.

**Answer:** True

**Why:** The atomic number Z uniquely identifies an element and equals the proton count. The mass number $A = Z + N$ also includes neutrons.

Page: https://tryals.app/practice/physics-i/atomic-structure-and-quantized-description/the-atomic-number-of-an-element-equals-the-number-of-protons-in-its

### 2. Electrons occupy discrete energy levels rather than a continuum. What observation forces that conclusion?

A. The atom would collapse without quantisation, which is a theoretical requirement
B. Electrons are too small to occupy a continuous range of positions
C. Chemical bonds form only at specific angles, which requires discrete levels
D. Emission spectra are sharp lines, not a continuous band

**Answer:** D. Emission spectra are sharp lines, not a continuous band

**Why:** The line spectrum is the direct evidence. Each line is one allowed transition, and the gaps between lines are the gaps between levels made visible.

Page: https://tryals.app/practice/physics-i/atomic-structure-and-quantized-description/electrons-occupy-discrete-energy-levels-rather-than-a-continuum-what

### 3. Heated hydrogen emits red light at **exactly 656 nm**: the same wavelength from a lab tube and from a distant galaxy. What fixes that number?

A. The size of the container, which selects the wavelengths that fit
B. The temperature of the gas, which sets the colour it glows
C. The density of the gas, which determines how often atoms collide
D. The energy gap between the $n = 3$ and $n = 2$ levels

**Answer:** D. The energy gap between the $n = 3$ and $n = 2$ levels

**Why:** A photon carries exactly the energy difference between two levels, and those levels are fixed by the atom. Temperature and density change how BRIGHT the line is and how many atoms are excited, never its wavelength; the container is irrelevant. That invariance is what makes spectroscopy work, the same 656 nm line identifies hydrogen anywhere in the universe.

Page: https://tryals.app/practice/physics-i/atomic-structure-and-quantized-description/heated-hydrogen-emits-red-light-at-exactly-656-nm-the-same

### 4. Which statements about isotopes are correct?

A. Same atomic number, different mass number
B. Different chemical properties from each other
C. Same number of protons, different number of neutrons
D. Same number of electrons in neutral atoms

**Answer:** A. Same atomic number, different mass number; C. Same number of protons, different number of neutrons; D. Same number of electrons in neutral atoms

**Why:** Isotopes have the same Z and electron count, so nearly identical chemistry. They differ only in neutron count and mass.

Page: https://tryals.app/practice/physics-i/atomic-structure-and-quantized-description/which-statements-about-isotopes-are-correct

### 5. The noble gases sit in one column and barely react at all. Why does a full outer shell produce chemical inertness?

A. Because they exist only as gases, and gases do not react
B. Because their nuclei are unusually stable against decay
C. Because a filled shell has nothing to gain by bonding
D. Because their atoms are too large for other atoms to approach

**Answer:** C. Because a filled shell has nothing to gain by bonding

**Why:** Reactivity is about available energy, not about the number of electrons. Xenon does react under force with fluorine, which shows the inertness is a matter of degree rather than a prohibition.

Page: https://tryals.app/practice/physics-i/atomic-structure-and-quantized-description/the-noble-gases-sit-in-one-column-and-barely-react-at-all-why-does-a