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.