12
2 The Nature of Light
The key insight of quantum theory is that the quantisation of energy in a bound
system applies to every change between two states. Hence not only is the energy of
electrons quantised, so are the spins, the momenta, and also molecular vibrations
and rotations. There are some conditions under which this rule breaks down, of
course. The emission caused by the deceleration of electrons in a magnetic field is
not quantised (note that we are considering free electrons here, moving outside an
atomic shell), and the emission caused by the capture of electrons by an ion is also
nonquantised. (Note again that the electron starts off free rather than bound—this
is what makes all the difference.) The emission of photons due to the capture of
electrons by atoms is called free-bound emission.
When the idea is applied to processes within our Sun, quantisation leads to
an important realisation. The Sun’s core temperature is extremely high, around
15 million K. As a result, the material inside it is in a highly ionised state—the
Sun is composed of plasma. This means that most emission is of the free-bound
variety, so the Sun should exhibit a continuous emission spectrum.
But it doesn’t. The Sun actually has some bright emission lines such as the Balmer
and Lyman series.
What is going on? The answer lies in the fact that whilst the emission of photons
has no dependency on direction, the absorption of photons does have a directional
bias. As photons near the star’s surface, there is more star below them than above, so
by this point, when a photon is absorbed, that photon is most likely from somewhere
deeper inside the star. This causes dark features known as absorption lines to appear
in the star’s spectrum.
But also, given that a star’s surface is much cooler and less dense than its core, it is
possible for some bound absorption to occur at or near the surface. This will show up
as bright emission lines, such as the aforementioned Balmer and Lyman features. The
Balmer lines are caused by the transition of a hydrogen electron down to the level-2
energy state. The first Balmer line, called the H-α line, is seen at λ = 656.3 nm
(in the red area of the visual spectrum) and is caused by a 3-to-2 transition. The
second Balmer line, H-β represents the 4-to-2 transition, and so on through the other
transitions.
The Lyman series covers the transitions down to the n = 1 energy level. The first,
the 2-to-1 transition, is called the Lyman α line.
When seen under laboratory conditions, an emission line will be narrow. What
broadening there is will be due partially to the optics used to observe it, and partially
to the uncertainty principle. However, actual stars are less tidy than well-organised
laboratories. Consequently, the thermal motion of the plasma within the star will
spread the lines out due to the Doppler effect. In addition, the bulk motion of the
plasma and also the motion of the target with respect to the observer (rotation, radial
velocity, etc.) will shift the line slightly toward either the blue or red end of the
spectrum. However, these effects don’t broaden the lines.
The quantisation of light is the underlying physics for the science of spectrography.
In Chaps. 14 and 15 we will go into this subject in much greater depth.
2 The Nature of Light
The key insight of quantum theory is that the quantisation of energy in a bound
system applies to every change between two states. Hence not only is the energy of
electrons quantised, so are the spins, the momenta, and also molecular vibrations
and rotations. There are some conditions under which this rule breaks down, of
course. The emission caused by the deceleration of electrons in a magnetic field is
not quantised (note that we are considering free electrons here, moving outside an
atomic shell), and the emission caused by the capture of electrons by an ion is also
nonquantised. (Note again that the electron starts off free rather than bound—this
is what makes all the difference.) The emission of photons due to the capture of
electrons by atoms is called free-bound emission.
When the idea is applied to processes within our Sun, quantisation leads to
an important realisation. The Sun’s core temperature is extremely high, around
15 million K. As a result, the material inside it is in a highly ionised state—the
Sun is composed of plasma. This means that most emission is of the free-bound
variety, so the Sun should exhibit a continuous emission spectrum.
But it doesn’t. The Sun actually has some bright emission lines such as the Balmer
and Lyman series.
What is going on? The answer lies in the fact that whilst the emission of photons
has no dependency on direction, the absorption of photons does have a directional
bias. As photons near the star’s surface, there is more star below them than above, so
by this point, when a photon is absorbed, that photon is most likely from somewhere
deeper inside the star. This causes dark features known as absorption lines to appear
in the star’s spectrum.
But also, given that a star’s surface is much cooler and less dense than its core, it is
possible for some bound absorption to occur at or near the surface. This will show up
as bright emission lines, such as the aforementioned Balmer and Lyman features. The
Balmer lines are caused by the transition of a hydrogen electron down to the level-2
energy state. The first Balmer line, called the H-α line, is seen at λ = 656.3 nm
(in the red area of the visual spectrum) and is caused by a 3-to-2 transition. The
second Balmer line, H-β represents the 4-to-2 transition, and so on through the other
transitions.
The Lyman series covers the transitions down to the n = 1 energy level. The first,
the 2-to-1 transition, is called the Lyman α line.
When seen under laboratory conditions, an emission line will be narrow. What
broadening there is will be due partially to the optics used to observe it, and partially
to the uncertainty principle. However, actual stars are less tidy than well-organised
laboratories. Consequently, the thermal motion of the plasma within the star will
spread the lines out due to the Doppler effect. In addition, the bulk motion of the
plasma and also the motion of the target with respect to the observer (rotation, radial
velocity, etc.) will shift the line slightly toward either the blue or red end of the
spectrum. However, these effects don’t broaden the lines.
The quantisation of light is the underlying physics for the science of spectrography.
In Chaps. 14 and 15 we will go into this subject in much greater depth.