an electron’s orbit is stable and constant. (By using the term stationary, Bohr did not
mean that the electrons stood still, but rather that their orbital radii and energies
remained constant.)
In Bohr’s model, both the orbital radius of an electron and the total energy of its orbit are
quantized. Electrons can only exist at certain distances from the nucleus that
correspond to certain energy levels. (Bohr used the concept of angular momentum to
determine the sizes of the orbits.) His model also led to the conclusion that an electron
in such an orbit does not radiate energy continuously and that its orbital radius cannot
gradually decay, but remains constant unless it is disturbed.
In Concept 2 we show a table of energy levels for a hydrogen atom. The lowest energy
level is called the ground-state energy level. At this level, the electron is at its closest to
the nucleus, and this distance is called the Bohr radius. This is the smallest possible
orbit of the electron. The ground-state energy of a hydrogen atom is í13.6 electron
volts.
Note that the value is negative. Physicists liken this to an electron being placed in a
well. It takes 13.6 eV to remove the electron from the atom so that it is free, no longer
bound to the proton that is the nucleus of the hydrogen atom. The closer it is to the
nucleus, the more negative its energy. This is akin to measuring the gravitational
potential energy of, say, a rock at the bottom of a well. Its gravitational potential energy
is stated to be negative there, and it becomes less negative as it approaches the top of
the well at the surface of the Earth.
Today, electrons are not considered to be particles moving like satellites in orbits
around the nucleus, and a quantum-physics electron cloud model of the atom has
replaced the Bohr model. Nevertheless, many of Bohr’s ideas have proven to be very
useful, and his model greatly advanced the understanding of the atom.
How does Bohr’s work relate to spectral lines? His model provided the first steps toward
a quantized view of the atom. As an electron moves between specific energy levels, it
emits or absorbs a quantized amount of energy in the form of a single photon of a
specific frequency.
The spectral lines that result when a gas emits or absorbs energy are thus also
quantized. Bohr’s work provided a model on the atomic side of why this should be the
case.When an electron moves from N 3
to N 2 , what happens to its
energy? Calculate the change in
energy of the atom.
ǻE = EfíEi
ǻE = (í3.40 eV) í (í1.51 eV)
ǻE = í1.89 eV
By how much does the atom’s
energy change when the photon
strikes, moving the electron from
N 1 to N 3?
ǻE = EfíEi
ǻE = (í1.51 eV) í (í13.6 eV)
ǻE = 12.1 eV
36.9 - Energy levels, photons and spectral lines
The Bohr model, combined with Einstein’s and
Planck’s work, explained the discrete spectral lines
that physicists were observing.
Why does excited hydrogen gas only emit light at
certain frequencies? When it is excited, say by heat,
or by an electric current, its atoms absorb energy.
When a hydrogen atom absorbs energy, its electron
jumps from one orbit to another, from a lower energy
level to a higher one. The change in energy is
quantized because electrons can only exist at the
specific energy levels prescribed in Bohr’s model.
When the atom loses energy, it does so by releasing
a single photon. The energy of the photon
corresponds to the amount of energy the electron loses as it returns to a lower-energy orbit.The energy of the photons emitted by excited gas atoms must be quantized because the electron energy levels are quantized. The frequency
of a photon is proportional to its energy, f = E/h. We perceive a given frequency (or wavelength) of light as a specific color.
For example, consider the red-colored line having wavelength 656 nm and frequency 4.57×10^14 Hz in the emission spectrum of hydrogen. A
photon of this color must have energy 3.03×10í^19 J, or 1.89 eV.It is possible to calculate the orbital change of the electron in a hydrogen atom that creates light of this frequency. An electron in the n = 3orbit
hasí1.51 eV of energy. An electron in the n = 2 orbit has í3.40 eV of energy. An electron that drops from N 3 to N 2 gives up 1.89 eV of
energy: exactly the energy of the red-color photon. A mystery solved! Some Nobels won!Hot, excited metal atoms emit light at characteristic frequencies. For example,
fireworks packed with copper salts radiate blue light when they explode.(^670) Copyright 2007 Kinetic Books Co. Chapter 36