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Key equations

Wien’s displacement law λ max T = 2.898 × 10 3 m K
Stefan’s law P ( T ) = σ A T 4
Planck’s constant h = 6.626 × 10 34 J s = 4.136 × 10 15 eV s
Energy quantum of radiation Δ E = h f
Planck’s blackbody radiation law I ( λ , T ) = 2 π h c 2 λ 5 1 e h c / λ k B T 1
Maximum kinetic energy
of a photoelectron
K max = e Δ V s
Energy of a photon E f = h f
Energy balance for photoelectron K max = h f ϕ
Cut-off frequency f c = ϕ h
Relativistic invariant
energy equation
E 2 = p 2 c 2 + m 0 2 c 4
Energy-momentum relation
for photon
p f = E f c
Energy of a photon E f = h f = h c λ
Magnitude of photon’s momentum p f = h λ
Photon’s linear
momentum vector
p f = k
The Compton wavelength
of an electron
λ c = h m 0 c = 0.00243 nm
The Compton shift Δ λ = λ c ( 1 cos θ )
The Balmer formula 1 λ = R H ( 1 2 2 1 n 2 )
The Rydberg formula 1 λ = R H ( 1 n f 2 1 n i 2 ) , n i = n f + 1 , n f + 2 ,
Bohr’s first quantization condition L n = n , n = 1 , 2 ,
Bohr’s second quantization condition h f = | E n E m |
Bohr’s radius of hydrogen a 0 = 4 π ε 0 2 m e e 2 = 0.529 Å
Bohr’s radius of the n th orbit r n = a 0 n 2
Ground-state energy value,
ionization limit
E 0 = 1 8 ε 0 2 m e e 4 h 2 = 13.6 eV
Electron’s energy in
the n th orbit
E n = E 0 1 n 2
Ground state energy of
hydrogen
E 1 = E 0 = 13.6 eV
The n th orbit of
hydrogen-like ion
r n = a 0 Z n 2
The n th energy
of hydrogen-like ion
E n = Z 2 E 0 1 n 2
Energy of a matter wave E = h f
The de Broglie wavelength λ = h p
The frequency-wavelength relation
for matter waves
λ f = c β
Heisenberg’s uncertainty principle Δ x Δ p 1 2

Conceptual questions

Give an example of an experiment in which light behaves as waves. Give an example of an experiment in which light behaves as a stream of photons.

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Discuss: How does the interference of water waves differ from the interference of electrons? How are they analogous?

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Give at least one argument in support of the matter-wave hypothesis.

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Give at least one argument in support of the particle-nature of radiation.

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Explain the importance of the Young double-slit experiment.

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Does the Heisenberg uncertainty principle allow a particle to be at rest in a designated region in space?

yes

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Can the de Broglie wavelength of a particle be known exactly?

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Do the photons of red light produce better resolution in a microscope than blue light photons? Explain.

yes

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Discuss the main difference between an SEM and a TEM.

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Problems

An AM radio transmitter radiates 500 kW at a frequency of 760 kHz. How many photons per second does the emitter emit?

9.929 × 10 32

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Find the Lorentz factor γ and de Broglie’s wavelength for a 50-GeV electron in a particle accelerator.

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Find the Lorentz factor γ and de Broglie’s wavelength for a 1.0-TeV proton in a particle accelerator.

γ = 1 060 ; 0.00124 fm

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What is the kinetic energy of a 0.01-nm electron in a TEM?

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If electron is to be diffracted significantly by a crystal, its wavelength must be about equal to the spacing, d , of crystalline planes. Assuming d = 0.250 nm , estimate the potential difference through which an electron must be accelerated from rest if it is to be diffracted by these planes.

24.11 V

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X-rays form ionizing radiation that is dangerous to living tissue and undetectable to the human eye. Suppose that a student researcher working in an X-ray diffraction laboratory is accidentally exposed to a fatal dose of radiation. Calculate the temperature increase of the researcher under the following conditions: the energy of X-ray photons is 200 keV and the researcher absorbs 4 × 10 13 photons per each kilogram of body weight during the exposure. Assume that the specific heat of the student’s body is 0.83 kcal / kg · K .

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Questions & Answers

what is biology
Hajah Reply
the study of living organisms and their interactions with one another and their environments
AI-Robot
what is biology
Victoria Reply
HOW CAN MAN ORGAN FUNCTION
Alfred Reply
the diagram of the digestive system
Assiatu Reply
allimentary cannel
Ogenrwot
How does twins formed
William Reply
They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
Oluwatobi
what is genetics
Josephine Reply
Genetics is the study of heredity
Misack
how does twins formed?
Misack
What is manual
Hassan Reply
discuss biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles
Joseph Reply
what is biology
Yousuf Reply
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
Joseph Reply
what is the blood cells
Shaker Reply
list any five characteristics of the blood cells
Shaker
lack electricity and its more savely than electronic microscope because its naturally by using of light
Abdullahi Reply
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
Ramadan
What is classification
ISCONT Reply
is organisms that are similar into groups called tara
Yamosa
in what situation (s) would be the use of a scanning electron microscope be ideal and why?
Kenna Reply
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
Hilary
cell is the building block of life.
Condoleezza Reply
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Practice Key Terms 4

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Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
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