2014/5/27

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PHYS 1CPROBLEM SESSION

COURSE INSTRUCTOR: DR. FRANK WUERTHWEIN

We’ll start at 7:00Week 9

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Problem Sessions

Office Hours (5-8 pm @ tutorial center)

Week 10 – June 3rd (Last time)

Week 9 – May 28th (Wed) Week 10 – June 2nd (Mon) (Last time)

No PB sessions / office hours during the final week (Jun 9 – Jun 13)

2014/5/27

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Quick Review

• Photoelectric effect

• Compton Scattering

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𝐸 = ℎ𝑓

Quick Review

Matter Wave

Uncertainty Principle

Wave Function

Particle In a Box

Hydrogen Atom

∆λ = λ′ − λ0 =ℎ

𝑚𝑒𝑐(1 − 𝑐𝑜𝑠𝜃)

Matter Wave

• de Broglie wavelength

• Reminder:

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λ =ℎ

𝑝

𝑝 = 𝑚𝑣 𝐸 = ℎ𝑓&

Quick Review

Matter Wave

Uncertainty Principle

Wave Function

Particle In a Box

Hydrogen Atom

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Ch28

Example 28.5

5• (1) 7.27x10-11 m, (2) 3.3x10-34 m

1. Calculate the de Broglie wavelength for an electron (me =

9.11x10-31 kg) moving at 1.00 x 107 m/s.

2. A rock of mass 50g is thrown with a speed of 40 m/s.

What is its de Broglie wavelength?

Ch28

Question 8

6

• (C)

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Ch28

Question 17

7• (d) > (e) = (a) > (b) > (c)

Uncertainty Principle

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∆𝑥 ∙ ∆𝑝 ≥ℎ

4𝜋

∆𝐸 ∙ ∆𝑡 ≥ℎ

4𝜋

ћ =ℎ

2𝜋

• Position & Momentum:

• Energy & Time:

• Sometimes we use the symbol ћ:

Quick Review

Matter Wave

Uncertainty Principle

Wave Function

Particle In a Box

Hydrogen Atom

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Ch28

Question 16

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• (a) (c)

Ch28

Question 18

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• (C)

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Ch28

Example 28.7

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• 0.385 mm

The speed of an electron is measured to be 5.00x103 m/s to

an accuracy of 0.00300%. Find the minimum uncertainty in

determining the position of this electron.

Wave FunctionProbability Amplitude / Density

• Wave function

= Probability amplitude

• Probability density

• Probability of finding the particle

- somewhere between 𝒂 ≤ 𝒙 ≤ 𝒃

- somewhere along the entire x axis12

ψ(𝑥)

ψ 𝑥 2

Quick Review

Matter Wave

Uncertainty Principle

Wave Function

Particle In a Box

Hydrogen Atom

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Ch28

Question 4

13• (e)

Ch28

Question 15

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• (d)

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• Boundary condition: ψ(x) = 0 at the walls

• Infinite numbers of solutions for ψ(x):

• |ψ(x)|2 gives the probability density of the

particle inside the box (varies with n).

• Draw them. 15

ψ𝑛(𝑥) =2

𝐿sin(

𝑛𝜋𝑥

𝐿)

Particle in a BoxWave Functions Quick Review

Matter Wave

Uncertainty Principle

Wave Function

Particle In a Box

Hydrogen Atom

Ch28

Question 10

16• (d)

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• Energy of the state ψ(x):

• n = 1, 2, 3, …

• The momentum (or velocity) of the

particle inside the box can be obtained by

relation 𝑬𝒏 =𝑷𝒏𝟐

𝟐𝒎. 17

𝐸𝑛 =ℎ2

8𝑚𝐿2𝑛2

Particle in a BoxEnergy Levels Quick Review

Matter Wave

Uncertainty Principle

Wave Function

Particle In a Box

Hydrogen Atom

Ch28

Question 9

18

• b > a > c > e > d

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Ch28

Example 28.8

19• (1) 9.42 eV, 37.7 eV, 84.8 eV (2) 1.82 x 106 m/s

1. An electron is confined between two impenetrable walls

0.200 nm apart. Determine the energy levels for the

states n = 1, 2, and 3.

2. Find the speed of the electron in the n = 1 state.

Ch28

Example 28.8

20• 6.63 x 10-36 m/s

3. A 0.500-kg baseball is confined between two rigid walls

of a stadium that can be modeled as a box of length 100

m. Calculate the minimum speed of the baseball.

Almost at rest!

(Do you really know how slow it is?)

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Hydrogen AtomQuantum Numbers

• Given n, there are n2 (n, l, ms) states.

• 2 electrons (ms = 1/2, -1/2) can be

assigned to a single (n, l, ms) state.

• We can assign 2n2 electrons to all

states with quantum number n.21

n = 1, 2, 3, 4, 5 …

l = 0, 1, 2, … , n-1

ml = -l , -l+1, … , l-1, l

ms = 1/2, -1/2

Quick Review

Matter Wave

Uncertainty Principle

Wave Function

Particle In a Box

Hydrogen Atom

Ch29

Question 6

22

• (e)

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Ch29

Question 9

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• (i) d (ii) c d (iii) b c

Ch29

Question 1

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• (e)

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Hydrogen AtomEnergy Levels

• Electron goes from higher energy level

EH to lower energy level EL by emitting a

photon with energy Ephoton = EH-EL.

• Electron jumps from lower energy level

EL to higher energy level EH by

absorbing energy equal to EH-EL

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𝐸𝑛 = −𝑘𝑒𝑒

2

2𝑎0

1

𝑛2= −

13.6

𝑛2(eV)

Quick Review

Matter Wave

Uncertainty Principle

Wave Function

Particle In a Box

Hydrogen Atom

Ch29

Question 3

26• (c)

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Ch29

Question 2

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• (a)

Hope to see you next week!

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