Formula Sheet: Structure of Atom

E is the energy (in joules) of a photon, h is Planck's constant (6.626 × 10⁻³⁴ J·s), and ν is the frequency (in Hz). This formula relates the energy of a photon to its frequency.

c is the speed of light (≈ 3 × 10⁸ m/s), ν is the frequency, and λ is the wavelength (in meters). This equation shows the relationship between the speed of light, its frequency, and wavelength.

ΔE is the change in energy during a transition, E_f is the energy of the final state, and E_i is the energy of the initial state. It indicates the energy difference when an electron transitions between energy levels.

E_n is the energy of the nth orbit in hydrogen, where n is the principal quantum number. This formula quantifies the energy of an electron in a certain orbit.

r_n is the radius of the nth orbit, n is the principal quantum number, and a₀ is the Bohr radius (52.9 pm). This relation describes how the radius of orbits expands as n increases.

Z_eff is the effective nuclear charge experienced by an electron, Z is the atomic number, and S is the shielding constant. This formula helps understand how inner electron shielding affects outer electron attraction.

λ is the de Broglie wavelength, h is Planck's constant, and p is the momentum of the particle (mass × velocity). This equation shows the wave-like properties of matter.

E is energy, m is mass (in kg), and c is the speed of light (≈ 3 × 10⁸ m/s). This formula expresses the equivalence of mass and energy, foundational to modern physics.

Where l is the azimuthal quantum number. This equation indicates how many orbitals exist within each subshell based on the shape defined by l.

An example of quantum numbers indicating the basic structure of atomic orbitals, where n is the principal quantum number and l is the azimuthal quantum number, defining the orbital shape.

ν_0 is the threshold frequency, W is the work function (energy needed to remove an electron), and h is Planck's constant. This equation defines the frequency required to emit electrons from a material.

K.E. is the kinetic energy of the emitted electron, and ν is the frequency of the incident light. This equation provides a link between incident light frequency and the energy of ejected electrons.

ΔE represents the energy difference between quantized states, h is Planck's constant, and f is the frequency of the emitted or absorbed radiation. This equation is crucial for understanding atomic transitions.

N is the total number of orbitals in a principal energy level, representing the filled and unfilled states based on the principal quantum number n. This equation provides a systematic approach to electron configuration.

This equation expresses the relationship of frequencies observed in the hydrogen spectrum transition from energy level n to ground state. It shows how spectral lines can be predicted.

E is the energy of an electron in hydrogen-like atoms, Z is the atomic number, and n is the principal quantum number. This equation helps calculate the energy levels specific to different atomic species.

E represents the total energy of a photon as it interacts with an electron, encompassing the work function (W) and the kinetic energy (K.E.) of the emitted electron after the reaction.

Where m is mass and v is velocity. This equation is also known as de Broglie equation, highlighting the wave-particle duality phenomenon, crucial for quantum mechanics understanding.

These combinations of quantum numbers help define the electronic structure of atoms, reflecting the arrangement of electrons within orbitals.

Summarizes that for a neutral atom, the atomic number (Z) is equal to the number of protons (P) minus electrons (with a negative charge). This is a foundational concept for atomic structure.