The Bohr Model of the Atom SPH4U

The Gold Foil Experiment Rutherford’s gold foil experiment demonstrated that the vast majority of a particles will pass through the foil and a few will be scattered by significant angles (even 180o).

The Gold Foil Experiment He concluded that the volume of the atom is mostly empty space and that most of the mass was contained in a small, dense nucleus.

The Gold Foil Experiment Further experiments demonstrated that Coulomb’s Law applies even at subatomic scales and that the positive charge on the nucleus is the same as the atomic number.

Spectra The continuous blackbody spectrum given off by a heated solid is caused by the interactions between neighbouring particles. Less-dense gases emit (or absorb) discrete wavelengths/frequencies.

Excitation An atom is normally found in its ground state (lowest energy). It can absorb the energy of incident photons and enter an excited state – but only for particular photon energies. It is the electrons in the atom that are moving to the excited state.

De-Excitation Some time later (spontaneously or by stimulated emission), the atom will return to its ground state by emitting a photon with the same frequency. Note that the wavelengths/frequencies of the emission and absorption lines are the same.

Energy-level Diagrams Energy-level diagrams are drawn as a series of horizontal lines with ground state on the bottom: Energy-level diagram for a hydrogen atom

Energy-level Diagrams Negative energy because the electron is bound.

Energy-level Diagrams At 0 eV, the electron is free, or “ionized.”

Energy-level Diagrams The difference between the ground state and ionization is the ionization energy. (Here, 13.6 eV.)

Excitation by Electrons Atoms can also be excited by collisions with electrons (which are scattered, not absorbed). The electrons will lose kinetic energy equal to the difference between the states. The difference between E2 and E1 is 10.2 eV. An electron with a kinetic energy of 11.2 eV would leave with 1 eV.

The Problem with “Orbits” Notice we say “energy levels” and not “orbits.” A centripetally accelerated electron would radiate energy as electromagnetic waves and spiral into the nucleus.

Standing Waves The “orbits” can best be understood as standing waves.

Standing Waves Only certain energies are allowed because only certain wavelengths “fit.” Fits Doesn’t fit

Bohr’s Quantum Hypothesis

What’s the radius of state n for Hydrogen?

What’s the radius of state n for Hydrogen? Solving one equation for speed and substituting:

What’s the radius of state n for Hydrogen? Solving one equation for speed and substituting: Substituting values for n = 1 yields r = 5.3 x 10-11 m, called the Bohr radius.

What’s the energy of state n for Hydrogen?

What’s the energy of state n for Hydrogen? Substituting derived expressions for the radius and speed

Hydrogen So for a hydrogen atom,

Example Determine the wavelength of the photon emitted when a hydrogen atom makes a transition from the n = 5 to the n = 2 state.

Example Determine the wavelength of the photon emitted when a hydrogen atom makes a transition from the n = 5 to the n = 2 state.

Example Determine the wavelength of the photon emitted when a hydrogen atom makes a transition from the n = 5 to the n = 2 state.

Example

Example

Example

Example This is the violet line in the visible (Balmer) spectrum.

More Practice “Another Look at Emission Spectra Activity” Textbook Questions p. 625 #4 p. 634 #10 p. 638 #8 p. 649 #2