Poetry of Physics and the Physics of Poetry

190 The Poetry of Physics and The Physics of Poetry

the photon p = E/c = hf/c = h/λ where we used the definition λ = cT = c/f
where T = 1/f is the period of the wave.
Although the relation between momentum and energy for the electron
is not the same as the photon, de Broglie assumed that the relation
between momentum and wavelength are the same. He, therefore,
concluded that the wavelength of the electron, λ, was also equal to h/p.
De Broglie applied his hypothesis of the wave nature of the electron to
the problem of Bohr’s atom and in particular to the question of how
stable orbits could be formed whose angular momentum was just equal
to an integer times h/2π. De Broglie assumed that the electrons orbiting
the nucleus of the atoms formed standing matter waves.
Let us digress for a moment and consider the standing waves of a
violin string, which is pinned down at its two ends. The violin string can
only vibrate in certain modes called standing waves. The condition on
the vibration is that an integer number of half-wave lengths fit into the
length of the string. Only these vibrations will reinforce themselves, after
they are reflected from the ends of the strings. Vibrations with different
wavelengths will interfere with their reflections from the end points and
quickly die out. Fig. 20.1 shows the standing waves for the three simplest
modes.

182 The Poetry of Physics and The Physics of Poetry

where T = 1/f is the period of the wave.

Although the relation between momentum and energy for the electron

is not the same as the photon, de Broglie assumed that the relation

between momentum and wavelength are the same. He, therefore,

concluded that the wavelength of the electron, !, was also equal to h/p.

De Broglie applied his hypothesis of the wave nature of the electron to

the problem of Bohr's atom and in particular to the question of how

stable orbits could be formed whose angular momentum was just equal

to an integer times h/2". De Broglie assumed that the electrons orbiting

the nucleus of the atoms formed standing matter waves.

Let us digress for a moment and consider the standing waves of a

violin string, which is pinned down at its two ends. The violin string can

only vibrate in certain modes called standing waves. The condition on

the vibration is that an integer number of half-wave lengths fit into the

length of the string. Only these vibrations will reinforce themselves, after

they are reflected from the ends of the strings. Vibrations with different

wavelengths will interfere with their reflections from the end points and

quickly die out. Fig. 20.1 shows the standing waves for the three simplest

modes.

Fig.20.1 Three Standing Waves

De Broglie argued that only those electron waves, which formed

circular standing waves and hence, could reinforce themselves would

form orbits. The condition for forming a circular standing wave is that

the wavelength fits into the circumference of the orbit an integer number

of times. In this way, the crest or maximum of the electron wave after

circling the orbit one time would match up with another crest and

reinforce itself. In the same manner, the trough or minimum of the wave

would also match after orbiting the circle one time. The condition that

Fig. 20.1 Three Standing Waves.

De Broglie argued that only those electron waves, which formed
circular standing waves and hence, could reinforce themselves would
form orbits. The condition for forming a circular standing wave is that
the wavelength fits into the circumference of the orbit an integer number
of times. In this way, the crest or maximum of the electron wave after
circling the orbit one time would match up with another crest and