Atoms. Physics Montwood High School R. Casao. More than 100 different elements have been discovered. Each element consists of atoms that contain: a number of protons Z, an equal number of electrons , and a number of neutrons N. The number of protons Z is called the atomic number.
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Montwood High School
Since electrons and protons have equal but opposite charges and there are an equal number of electrons and protons in the atom, atoms are electrically neutral.
The Bohr Model
Viewed through a spectroscope with a narrow-slit aperture, the light appears as a discrete set of lines of different colors and wavelengths.
Johann Balmer found that wavelengths of the lines in the visible spectrum of hydrogen can be represented by the formula
According to Bohr’s model, the electron of the hydrogen atom moves under the influence of the Coulomb attraction to the positive nucleus according to classical mechanics, which predicts circular or elliptical orbits with the force center at one focus.
Energy in a Circular Orbit
circular orbit of radius r about
a positive charge Z·e such as
the nucleus of a hydrogen
atom (Z = 1).
can be related to the radius of
The potential energy of the electron of charge –e at a distance r from a positive charge Z·e is:
Mechanical stability is achieved because the Coulomb attractive force provides the centripetal force necessary for the electron to remain in orbit.
An atom radiates only when the electron makes a transition from one allowed orbit (stationary orbit) to another.
The electron in the hydrogen atom can move only in certain nonradiating, circular orbits called stationary orbits.
To obtain the frequencies implied by the Rydberg-Ritz formula, the radii of stable orbits must be proportional to the squares of integers.
where n = 1, 2, …
ħ = = 1.055 x 10-34 J·s = 6.582 x 10-16 eV·s
The energies En with Z = 1 are the quantized allowed energies for the hydrogen atom.
and whose wavelength is
Since the energies are quantized, the frequencies and wavelengths of the radiation emitted by the hydrogen atom are quantized in agreement with the observed line spectrum.
The process of removing an electron from an atom is called ionization, and the energy required to remove the electron is the ionization energy.
Transitions from n2 = 3 to and n1 = 4, 5, 6, … are known as the Paschen series.
Problem example: determine the energy and wavelength of the line with the longest wavelength in the Lyman series.
The energy of the photon is the difference in the energies of the initial and final atomic state: