Quantization of light energy

Quantization of light energy
 Planck derived a formula that described the distribution of
wavelengths emitted, depending on the temperature.

His formula required that light could only be absorbed or emitted in
discrete chunks or quanta, whose energy depended on the
frequency or wavelength.
E  hf
where h = 6.626 x 10-34 J s
is called Planck’s constant.
 This idea was indeed radical.
 Einstein showed that the quantization of light energy
explains a number of other phenomena.
 Photoelectric effect.
 The idea of light quanta (photons) having energies E = hf
prepared the way for a new model of the atom.
Wave
 Moving one end of the Slinky back and forth created a local
compression where the rings of the spring are closer together
than in the rest of the Slinky.
 The slinky tries to return to equilibrium. But inertia cause the links to pass
beyond. This create a compression. Then the links comes back to the
equilibrium point due to the restoration force, i.e. the elastic force.
 The speed of the pulse may depend on factors such as
tension in the Slinky and the mass of the Slinky.
 If instead of moving your hand back and forth just once, you
continue to produce pulses, you will send a series of longitudinal
pulses down the Slinky.

If equal time intervals separate the pulses, you produce a periodic
wave.

The time between pulses is the period T of the wave.

The number of pulses or cycles per unit of time is the frequency f = 1/T.

The distance between the same points on successive pulses is the
wavelength .

A pulse travels a distance of one wavelength in a time of one period.

The speed is then the wavelength divided by the period:

v  f
T
 The pulse we have been discussing is a
longitudinal wave: the displacement or
disturbance in the medium is parallel to the
direction of travel of the wave or pulse.
 Transverse wave
 Sound waves are longitudinal.
 Light waves are transverse.
A longitudinal wave traveling on a Slinky has a
period of 0.25 s and a wavelength of 30 cm.
What is the speed of the wave?
a)
b)
c)
d)
e)
0.25 cm/s
0.30 cm/s
1 cm/s
7.5 cm/s
120 cm/s
A longitudinal wave traveling on a Slinky has a
period of 0.25 s and a wavelength of 30 cm.
What is the frequency of the wave?
a)
b)
c)
d)
e)
0.25 Hz
0.30 Hz
0.83 Hz
1.2 Hz
4 Hz
A wave on a rope is shown below.
What is the wavelength of this wave?
a) 1/6 m
b) 1 m
c) 2 m
d) 3 m
e) 6 m
If the frequency of the wave is 2 Hz,
what is the wave speed?
a) 1/6 m/s
b) 2/3 m/s
c) 2 m/s
d) 3 m/s
e) 6 m/s
Blackbody Radiation
Quantization of light energy
 Planck derived a formula that described the distribution of
wavelengths emitted, depending on the temperature.

His formula required that light could only be absorbed or emitted in
discrete chunks or quanta, whose energy depended on the
frequency or wavelength.
E  hf
where h = 6.626 x 10-34 J s
is called Planck’s constant.
 This idea was indeed radical.
 Einstein showed that the quantization of light energy
explains a number of other phenomena.
 Photoelectric effect.
 The idea of light quanta (photons) having energies E = hf
prepared the way for a new model of the atom.
Bohr’s model of the atom
 Bohr combined all these ideas:




the discovery of the nucleus
knowledge of the electron
the regularities in the hydrogen
spectrum
the new quantum ideas of Planck and
Einstein
 He pictured the electron as orbiting
the nucleus in certain quasi-stable
orbits.
 Light is emitted when the electron
jumps from one orbit to another.
 The energy between the two orbits
determines the energy of the
emitted light quantum.
Bohr’s model of the atom
 The hydrogen spectrum
can be explained by
representing the
energies for the
different electron orbits
in an energy-level
diagram.
What is the wavelength of the photon emitted in
the transition from n = 4 to n = 2? Note: h =
6.626 x 10-34 J s = 4.14 x 10-15 eV s
A. 487 nm
B. 4000 nm
C. 12 nm
D. 66 nm
E. 2000000 nm
The Structure of the Nucleus
 Rutherford. Bombarded nitrogen gas with alpha particles



A new particle emerged We now call this particle a proton.
Charge +e = 1.6 x 10-19 C
Mass = 1/4 mass of alpha particle, 1835 x mass of electron
 Bothe and Becker bombarded thin beryllium samples
with alpha particles.


A very penetrating radiation was emitted.
Originally assumed to be gamma rays, this new radiation
proved to be even more penetrating.
 Chadwick determined it was a new particle which we
now call neutron.


No charge -- electrically neutral
Mass very close to the proton’s mass
 The basic building blocks of the nucleus are the proton and
the neutron.


Their masses are nearly equal.
The proton has a charge of +1e while the neutron is electrically neutral.
 This explains both the charge and the mass of the nucleus.

An alpha particle with charge +2e and mass 4 x mass of the proton is
composed of two protons and two neutrons.

A nitrogen nucleus with a mass 14 times the mass of a hydrogen
nucleus and a charge 7 times that of hydrogen is composed of seven
protons and seven neutrons.