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PH284
Lecture 1
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Cards (168)
What are the key characteristics of the 2N3904 transistor?
Small signal amplifier
Maximum collector current (I_C)
:
200 mA
Maximum collector-emitter voltage (V_CE)
:
40 V
Maximum base-emitter voltage (V_BE)
:
5 V
Low power dissipation
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What are the two assessment methods for PH284?
1st Attempt (Exemption):
20%
Continuous assessment
(
CA
)
40%
Semester 1 test
40% Semester 2 test
1st Attempt (Exam):
80%
Two-hour
April/May
exam
20% Continuous assessment (CA)
2nd Attempt:
100%
August
two-hour exam
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What is the primary content of the QP Syllabus?
Introduction to quantum effects,
De Broglie waves
and
uncertainty
, Infinite potential well, Potential steps, barriers, tunnelling, Quantum harmonic oscillator, and
quantum mechanics
in 2D and 3D
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What are Rayleigh-Jeans and Wien’s radiation laws?
Rayleigh-Jeans Law:
d
n
λ
=
dn_\lambda =
d
n
λ
=
(
8
π
λ
−
4
)
d
λ
(8 \pi \lambda^{-4}) \, d\lambda
(
8
π
λ
−
4
)
d
λ
U
λ
(
T
)
=
U_\lambda(T) =
U
λ
(
T
)
=
8
π
k
T
λ
−
4
8 \pi kT \lambda^{-4}
8
πk
T
λ
−
4
Predicts
ultraviolet
catastrophe at
short wavelengths
Works well for
long wavelengths
Wien’s Radiation Law:
U
λ
(
T
)
=
U_\lambda(T) =
U
λ
(
T
)
=
A
λ
−
5
e
−
B
/
(
λ
T
)
A \lambda^{-5} e^{-B/(\lambda T)}
A
λ
−
5
e
−
B
/
(
λ
T
)
Empirical with experimentally determined constants A and B
Works well for short wavelengths
Fails at long wavelengths
View source
How does the spectral radiance change as the temperature increases?
The spectral radiance increases at all wavelengths
The peak radiance shifts to shorter wavelengths (
Wien's displacement law
)
The total power radiated increases (
Stefan-Boltzmann law
)
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How does the experimental setup work for two-photon quantum imaging?
A
UV source
emits
position-correlated entangled photon pairs
One photon passes through the object to be imaged
The second photon is detected by a detector (e.g.,
bucket detector
)
The detected photon's position provides information about the first photon's path
The first photon's path through the object is used to construct the image
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What is the formula for the Compton shift?
λ
′
−
λ
=
\lambda' - \lambda =
λ
′
−
λ
=
λ
C
(
1
−
cos
(
θ
)
)
\lambda_C (1 - \cos(\theta))
λ
C
(
1
−
cos
(
θ
))
View source
What is the role of the second photon in two-photon quantum imaging?
It acts as a signal to determine the first
photon's
path and contributes to image construction
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What type of detector is commonly used to detect the second photon in two-photon quantum imaging?
Bucket detector
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Why might the class details and timetable be available via a link instead of directly on the study material?
To provide the most
current
and easily
accessible
information
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How did Planck derive his radiation law and what assumptions did he make?
Planck’s Derivation:
Planck thought of radiation as a series of
oscillators
.
He assumed each oscillator’s energy was
quantized
in units of
E
=
E =
E
=
h
f
h f
h
f
This led to:
U
λ
=
U_\lambda =
U
λ
=
8
π
h
c
λ
−
5
e
h
c
/
(
λ
k
T
)
−
1
\frac{8 \pi h c \lambda^{-5}}{e^{hc/(\lambda k T)} - 1}
e
h
c
/
(
λk
T
)
−
1
8
πh
c
λ
−
5
h
=
h =
h
=
6.63
×
1
0
−
34
J.s
6.63 \times 10^{-34} \, \text{J.s}
6.63
×
1
0
−
34
J.s
is
Planck’s constant
and
k
=
k =
k
=
1.38
×
1
0
−
23
J K
−
1
1.38 \times 10^{-23} \, \text{J K}^{-1}
1.38
×
1
0
−
23
J K
−
1
is
Boltzmann’s constant
.
Einstein’s
contribution:
Einstein added physical rigour to Planck’s assumption.
He showed each oscillator’s energy must be quantized as
E
n
=
E_n =
E
n
=
n
h
f
,
n h f,
nh
f
,
where n is an integer.
View source
What happens to the wavelength of maximum energy density as a body is heated?
The wavelength of maximum energy density
reduces.
View source
What is Wien’s displacement law formula?
λ
m
a
x
T
=
\lambda_{max} T =
λ
ma
x
T
=
2.90
×
1
0
−
3
m K
2.90 \times 10^{-3} \text{ m K}
2.90
×
1
0
−
3
m K
View source
What type of scientific instrument is shown in the image?
A
high-vacuum apparatus
Typically used for
surface science experiments
View source
Why is high vacuum important in such instruments?
It minimizes
collisions
with the
sample
, ensuring a clean surface
View source
What type of bits are used in quantum computers?
Quantum bits (
qubits
).
View source
What are the main components and roles in the tutorials?
Tutorials support
lectures
and practice
problem
solving.
One hour per week.
Mix of individual (
7.5%
) and group (7.5%) problems.
In the
first
week, students pick groups of 5 on
MyPlace
.
Each two-week block allocates a group problem and 4 individual MyPlace questions.
Weeks
1-3, 5, 7, 9 are for working through group problems.
Weeks 4, 6, 8, 10 are for groups to present solutions.
Groups can use
Onedrive
Documents for collaborative editing.
Roles include
presenter
,
solver
,
scribe
, and
checker
.
Group assembly and presentation of worked solutions enhance skills.
View source
What were some key observations that challenged classical physics?
The
elements
: Why are there
~100
elements and how do they form a
periodic table
?
Blackbody radiation
: Experimental spectra did not match theoretical models.
Photoelectric effect
: Experimental observations disagreed with classical predictions.
Compton effect
: X-rays scattered off crystals changed their wavelength unexpectedly.
Atomic structure
: Unclear about atoms ‘inside’ and why light from atomic vapour lamps was at discrete colours.
View source
How is the Stefan-Boltzmann law derived from Planck’s law?
By
integrating
Planck's law
View source
What can be measured in a photoelectric effect experiment?
The
photocurrent
as a function of
applied voltage
.
View source
What is the formula for the momentum of a photon?
p
=
p =
p
=
h
λ
\frac{h}{\lambda}
λ
h
View source
What is the formula for the angular momentum of an electron according to Bohr?
L
=
L =
L
=
m
e
v
r
=
m_e v r =
m
e
v
r
=
n
ℏ
n \hbar
n
ℏ
View source
What is the vector form of de Broglie’s equation?
p
=
p =
p
=
ℏ
k
⃗
\hbar \vec{k}
ℏ
k
View source
What is the formula for the de Broglie wavelength of an electron in terms of accelerating voltage?
λ
=
\lambda =
λ
=
h
2
m
q
V
\frac{h}{\sqrt{2 m q V}}
2
m
q
V
h
View source
What was observed about the scattering pattern of electrons?
Electrons were scattered strongly in one
direction
View source
What generates the electron beam?
Electron gun
(
heated wire
)
View source
How does the extra distance travelled by the electron beam parts relate to the lattice spacing?
2l
=
2d
sin(φ)
View source
What mathematical tools are used to describe matter waves in Quantum Physics?
Wavefunctions
Schrödinger equation
Complex numbers
Partial differential calculus
View source
What is the product of
z
1
=
z_1 =
z
1
=
1
−
3
i
1 - 3i
1
−
3
i
and the complex conjugate of
z
2
=
z_2 =
z
2
=
−
3
+
-3 +
−
3
+
4
i
?
4i?
4
i
?
15
+
5i
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What is the condition for constructive interference?
2d sin(φ)
=
n λ
for integer n
View source
Find the derivative of
f
(
x
)
=
f(x) =
f
(
x
)
=
tan
(
x
)
.
\tan(x).
tan
(
x
)
.
sec<sup>2</sup>
(x)
View source
Find the partial derivative
∂
f
∂
y
\frac{\partial f}{\partial y}
∂
y
∂
f
of
f
(
x
,
y
)
=
f(x, y) =
f
(
x
,
y
)
=
sin
(
π
x
+
2
π
y
)
.
\sin(\pi x + 2\pi y).
sin
(
π
x
+
2
π
y
)
.
2
π
cos
(
π
x
+
2
π
y
)
2\pi \cos(\pi x + 2\pi y)
2
π
cos
(
π
x
+
2
π
y
)
View source
What are the two standard forms of harmonic wave functions?
ψ
(
x
,
t
)
=
\psi(x, t) =
ψ
(
x
,
t
)
=
A
sin
(
k
x
−
ω
t
)
+
A \sin(kx - \omega t) +
A
sin
(
k
x
−
ω
t
)
+
B
cos
(
k
x
−
ω
t
)
B \cos(kx - \omega t)
B
cos
(
k
x
−
ω
t
)
A
e
i
(
k
x
−
ω
t
)
A e^{i(kx - \omega t)}
A
e
i
(
k
x
−
ω
t
)
View source
How does the Born interpretation relate the wave function to the probability of finding a particle?
The square of the amplitude of the wave function
(
∣
ψ
∣
2
)
(|\psi|^2)
(
∣
ψ
∣
2
)
gives the
probability density
Integrating this over a region gives the probability of finding the particle in that region
View source
Write the general form of a harmonic wave function.
ψ
(
x
,
t
)
=
\psi(x, t) =
ψ
(
x
,
t
)
=
A
e
i
(
k
x
−
ω
t
)
A e^{i(kx - \omega t)}
A
e
i
(
k
x
−
ω
t
)
View source
Express
z
=
z =
z
=
5
e
−
i
arctan
(
4
/
3
)
5 e^{-i \arctan(4/3)}
5
e
−
i
a
r
c
t
a
n
(
4/3
)
in Cartesian form.
3 - 4i
View source
Why is
f
′
(
x
)
=
f'(x) =
f
′
(
x
)
=
sec
2
(
x
)
\sec^2(x)
sec
2
(
x
)
true for
f
(
x
)
=
f(x) =
f
(
x
)
=
tan
(
x
)
?
\tan(x)?
tan
(
x
)?
Using the
product rule
and
trigonometric
identities
View source
What is the formula for the allowed energies of a Hydrogenic atom according to Bohr?
E
n
=
E_n =
E
n
=
−
Z
2
e
2
8
π
ϵ
0
a
0
n
2
=
-\frac{Z^2 e^2}{8\pi \epsilon_0 a_0 n^2} =
−
8
π
ϵ
0
a
0
n
2
Z
2
e
2
=
−
Z
2
×
13.6
eV
n
2
-\frac{Z^2 \times 13.6 \text{ eV}}{n^2}
−
n
2
Z
2
×
13.6
eV
View source
What mathematical tools are used to describe matter waves in Quantum Physics?
Wavefunctions
Schrödinger equation
Complex numbers
Partial differential calculus
View source
What type of image is produced in two-photon quantum imaging?
Upright image
View source
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