Page 24 - Spotlight A+ Physics Form 4.5

Form
5
Chapter 7 Quantum Physics Physics
Example 1 6. The relationship between the momentum of
particle, p and its wavelength, λ is
Calculate the photon energy for light with
wavelengths 450 nm and 700 nm. Compare both λ = —–
h
photons. p
Solution which h is Planck’s constant (6.63 × 10 J s)
–34
Planck’s constant, h = 6.63 × 10 J s
–34
Speed of light in vacuum, c = 3.00 × 10 m s
–1
8
Wavelength, λ = 450 × 10 m
–9
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Wavelength, λ = 700 × 10 m
–9
2 2
p
hc
(mv)
1
m
2
E = hf = —— K = —mv × —– ➞ K = ——— = ——
2
λ 2 m 2m 2m
Photon energy of 450 nm: which p = mv, p = ABBBB
2mK
8
1
E = 6.63 × 10 –34 3.00 × 10 –9 2
—————–
1 450 × 10
= 4.42 × 10 J 7. The larger the momentum of particle, the shorter
–19
Photon energy of 700 nm: the wavelength produced. The momentum of
p
2
8
1
E = 6.63 × 10 –34 3.00 × 10 –9 2 particle is p = mv, then —— = K
—————–
2 700 × 10 2m
= 2.84 × 10 J
–19
h
h
The shorter the wavelength of light, the higher λ = —–– = ————
mv
ABBBB
the photon energy. 2mK
where m is the mass of particle, v is the velocity
of particle and K is the kinetic energy of particle.
Wave-Particle Duality 8. Since the value of h is too small, the particle
with large mass will have too short of de Broglie
wavelength to be detected. Thus, the wave
characteristics cannot be observed.
Wavelength simulation 9. In 1927, the presence of wave properties of
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electrons was confirmed through the electron
diffraction experiments.
1. Light has wave properties because it shows the 10. Photograph 7.1 shows the diffraction pattern of
phenomena of diffraction and interference. electrons through a thin layer of graphite. The
pattern in Photograph 7.2 resembles the light
2. Object has particle properties because it has diffraction pattern through an aperture.
momentum, kinetic energy and also collide with
each other.
3. Louis de Broglie introduced a hypothesis states
that all particles can exhibit wave characteristics
in year 1924.
4. However, it is experimentally difficult to show
the wave characteristics of particles with large
masses.
5. Thus, Louis de Broglie predicted that the wave Photograph 7.1 Photograph 7.2
characteristics can be shown by light particles 11. This observation proved de Broglie’s hypothesis. CHAP
such as electron, proton and neutron. 7
7.1.3 477