Quantum models have changed how we see atoms. Two important ideas in this are wave-particle duality and energy levels that can only exist in certain amounts.

Important Ideas:

1. Wave-Particle Duality:

   • In 1924, a scientist named Louis de Broglie suggested that tiny particles, like electrons, can behave like both waves and particles.
   • The “de Broglie wavelength” is a way to measure this, and it’s described by the formula: $\lambda = \dfrac{h}{p}$ Here, $h$ is a really small number called Planck's constant ($6.63 \times 10^{-34} \ \text{Js}$), and $p$ stands for the momentum of the particle.

2. Quantum Mechanical Model:

   • In 1926, another scientist named Schrödinger developed a model that uses something called wave functions ($\Psi$). These functions help us understand how electrons act in atoms.
   • When we look at the square of the wave function, $|\Psi|^2$, it shows us where we might find an electron around the nucleus.

3. Energy Levels:

   • Electrons are found in specific energy levels, which are identified using quantum numbers. The main quantum number ($n$) tells us which energy level an electron is in. For example, $n=1, 2, 3,...$ represent the first seven energy levels.
   • For an electron in a hydrogen atom, the energy is calculated like this: $E_n = -\dfrac{13.6\, \text{eV}}{n^2}$
   • These specific energy levels explain why atoms can give off or take in light at certain colors when electrons jump between levels.

Electron Movements:

• When an electron jumps from one energy level to another, it either takes in or gives off a tiny packet of energy called a photon. The energy of this photon equals the difference between the two levels: $E_{photon} = E_{final} - E_{initial}$
• This idea is important for spectroscopy, which helps scientists figure out what elements are present by looking at the light they emit or absorb.

Conclusion:

Quantum models have improved upon the older Bohr model. They give us a better understanding of how atoms work and how chemical bonds form. This has greatly influenced modern atomic theory and chemistry.