Download Chapter 2. The fundamental laws of Mechanics

Appendix
Brief Review to Medical Physics
Chapter 1. Introduction to Physics
In this chapter and for the first part, you should be able to answer some of simple
questions about physics, fundamental quantities in SI unit, standard units used in
physics, rounding off numbers and scientific notation. In the second part of this
chapter, you should be able to do the dot product and cross product of two vectors and
of course you should also be able to do some differentiation to some simple functions
as you have learned advanced mathematics.
Important concepts and formulae:
Example 1.1 The fundamental quantities in physics are time, length, mass, Electric
current, temperature, amount of a substance and luminous intensity, and their
corresponding units in SI system are second, meter, kilogram, Ampere, Kelvin, Mole
and candela.

 





Example 1.2* Suppose we have two vectors: A  2i  4 j  2k , B  8i  2 j  4k ,
find: (1) the magnitude of the two vectors; (2) the dot product of the two vectors; (3)
the angle between the two vectors (4) the sum of the two vectors; (5) magnitude of the
cross product of the two vectors.

 





If A  a x i  a y j  a z k , B  bx i  b y j  bz k , in order to finish the above problem,
the formulas you need are:

Magnitude of vector A :
Dot product:

A  A  a x2  a y2  a z2
(1.1)
 
A  B  a x bx  a y b y  a z bz
(1.2)
 
 
A B
Included angle between vectors: A  B  AB cos  cos 
AB
  
if F  A  B then Fi  Ai  Bi
Sum of vectors:
(1.3)
(1.4)

 


Cross product: A  B  (a y bz  a z b y )i  (a z bx  a x bz ) j  (a x b y  a y bx )k (1.5)
Amplitude of cross product:
 
A  B  AB sin 
(1.6)
where  in (1.6) can be determined by (1.3) or calculated using (1.5).
Example 1.3 About the differentiations, you should understand that the meaning of
153
the differentiation to a function can be the slope of a function at a particular point, the
speed or acceleration of an object depending on the property of the function, and
should remember the following formulae:
 
d n
x  nx n 1 ;
dx
d
sin( x  4)   cos(x  4);
dx
d
cos(x  4)   sin( x  4)
dx
(1.7)
Chapter 2. The fundamental laws of Mechanics
In this chapter, more contents are included. You should know that (1) the
description methods of motion, (2) the concepts of displacement, velocity,
acceleration, angular velocity, angular acceleration, tangential velocity and
acceleration and angular momentum, (3) Newton’s law of motion and rotational law*,
(4)* conservational law of momentum, energy, and angular momentum.
Important concepts and formulae:
1. Equation of motion:




r (t )  x(t )i  y(t ) j  z (t )k
(2.1)
The instantaneous velocity and acceleration are given as


dr (t ) dx  dy  dz 
v (t ) 

i
j  k,
dt
dt
dt
dt



dv (t ) d 2 r (t ) d 2 x  d 2 y  d 2 z 
a (t ) 

 2 i  2 j 2 k
dt
dt 2
dt
dt
dt
(2.2)
(2.3)
Here you should be clear that the displacement, the velocity and acceleration are
vectors. They are determined by both of magnitudes and directions.
2. Newton’s laws of motion






dp d
dv
 (mv )  m
 ma
a) Fnet  0. b) Fnet 
(2.4)
dt dt
dt


c) FA due to B   FB due to A
(2.5)
3. Work and Energy
a) Work:
b 

Aab   F  dr
a
b) Kinetic energy and potential energy (see Chinese text book on page 9-10)
c) Conservation of energy in a system
E  K  U = Constant.
4. Rotational motion
154
a) Angular displacement ,
d
b) angular velocity  
,
dt
c) tangential velocity = curvature radius  angular velocity
 v  r
d) Angular acceleration:  
(2.6)
(2.7)
d d 2
 2
dt
dt
(2.8)
e) tangential acceleration = curvature radius  angular acceleration:
(2.9)
a  r
  
f) Angular momentum: L  r  p , the amplitude of the momentum is
  
L  r  p  r  p sin 
(2.10)
Chapter 3. Fluid Dynamics
In this chapter, there are several concepts in hydrostatics you should know. They are
the pressure, the Pascal’s principle, Buoyancy and Archimedes’ principle. However,
Hydrodynamics is much more important than the hydrostatics for you. The concepts
and equations involved in hydrodynamics are steady flow, ideal fluid, continuity
equation, Bernoulli’s equation, laminar flow, viscosity, Reynolds number, Poiseuille’s
law and Stokes law:
Important concepts and formulae:
F
A
1. Pressure:
p
2. Pascal’s principle
F1 F2

A1 A2
3. Archimedes’ principle:
FB    g  V
 is density of fluid, g is the gravitational acceleration and V is the volume of the
body in liquid.
4. Ideal fluid:
The properties of ideal fluid are
a) non-viscous,
b) incompressible and
c) moving in a streamline motion.
5. Continuity equation:
Av = Constant.
The velocity of the fluid is inversely proportional to the cross-sectional area.
6. Bernoulli’s equation:
155
1
 v 2   gh = Constant.
2
For a horizontal flow, h can be chosen as zero, we have
1
p   v 2 = Constant
2
When v is big, the pressure will be small, vice versa.
7. *Applications to Bernoulli’s equation:
a) Kinemometer,
b) The Pitot tube
8. *The flow of viscous fluid:
a) Laminar flow,
b) Reynolds number,
c) Poiseuille’s Law and Stokes’ Law.
p
Chapter 4. Vibrations and Waves
In this chapter, you need to master (1) the basic laws of simple harmonic motion, (2)
the method of the superposition of two simple harmonic motions, (3) the propagation
regularity of waves, (4) the physical meaning of wave equation, and (5) the
phenomenon and laws of the interference of waves, and to understand (a) the
formation of standing waves, (b) the basic concept of acoustics (声学), (c) the sound
intensity level and loudness level, and (d) the characteristics of ultrasound and its
applications to medicine.
Important concepts and formulae:
1. The equation of SHM
x  A cos(t   )
or
x  A sin( t   )
2. The velocity and acceleration of SHM
(1) Velocity of SHM:
dx
v
  A sin( t   )
dt
(2) Acceleration of SHM
a
dv d 2 x

  A 2 cos(t   )
dt dt 2
(4.1)
(4.2)
(4.3)
3. The characteristic quantities of SHM
(1) The amplitude: A; the angular frequency: ; and the initial phase: .
(2) The period and frequency of SHM:
(a) The period is the time taken for completing one complete vibration,
denoted by T. Obviously
2

(4.4)
T
156
(b) The frequency, denoted by f or , is the number of complete vibrations in
one second. Therefore,
1 
f  
(4.5)
T 2
(3) The amplitude and initial phase can be determined by initial conditions which
are initial displacement of SHM x0 and initial speed v0:
v02
A x 
2
0

2

v 

 x 0 
  arctan  -
,
(4.6)
4. The energy of SHM
(1) The kinetic energy of SHM
2
Ek 
1 2 1  dx 
1
mv  m   m 2 A 2 sin 2 t   
2
2  dt 
2
(4.7)
(2) The potential energy of SHM
1 2 1 2
kx  kA cos 2 t   
2
2
1
 m 2 A 2 cos 2 t   
2
Ep 
(4.8)
k
m
(3) The total energy of the SHM system
1
1
E  E k  E p  m 2 A 2  kA2
2
2
The total energy does not change with time, so it is conservative.
5*. Damped vibration, forced vibration and resonance
(1) Features of damped vibration:
(a) The amplitude decreases
where
2 
(b) The period increases
T
2
 
2
0
2
.
(4.9)
(4.10)
(2) Forced vibration:
(a) External force: F  Fm cos t
(b) Equation of damped vibration: x  Acost   
(c) Amplitude of damped vibration: A 
Fm


m  02   2  4  2 2
2
 2  

2
2 
 0   
  arctan 
(d) The initial phase:
(3) Resonance:
157
(4.11)
(4.12)
(a) Angular frequency of resonance: esonance  02  2 2 ,
(b) Amplitude of resonance: Aresonance 
Fm
(4.13)
(0) (4.14)
2m  02   2
6. Composition of SHM
(1) The addition of two vibrations with same vibrational directions and same
frequencies
(a) Two original vibrations: x1  A1 cost  1 , x2  A2 cost   2 
(b) The resultant vibration: x  A cos(t   ) with
A12  A22  2 A1 A2 cos(1   2 ) ,
A
tan  
(4.15)
A1 sin 1  A2 sin  2
.
A1 cos 1  A2 cos  2
(4.16)
(c) Two special cases:
  1  2  2k
(k =0, 1, 2, …), A  A1  A2
  1  2  (2k  1) ,
(k =0, 1, 2,…),
(4.17)
A  A1  A2 (4.18)
7. The composition of two vibrations with the same frequency but orthogonal
vibrational directions
(1) Two original vibrations: x  A1 cost  1 , y  A2 cost  2 
(2) The compositional orbital equation in x-y plane is given as
x 2 y 2 2 xy
 2
cos( 2  1 )  sin 2  2  1 
2
A1 A2 A1 A2
(a) 2  1  2k
y
(k = 0, 1, …)
A2
x
A1
(b) 2  1  (2k  1)
y
(4.20)
(k = 0, 1, …)
A2
x
A1
1
(c)  2  1  (2k  )
2
(4.19)
(4.21)
(k = 0, 1, …)
158
(4.22)
2
2
 x  y 
      1
 A1   A2 
(4.23)
(d) Go back to the original equations to determine the rotational direction for
the particle.
8. Wave motion and propagation
(1) Wave front, wave line, amplitude A, wave period T, wave frequency f, the
propagating speed of waves u, the angular frequency  of wave, and wave
number k. They have the following relations.
2
λ
2
2
T
, u ,
f 
,
k
.
(4.24)

T


(2) Wave equation has quite a few forms. These forms are obtained by the above
relations between the characteristic quantities:
  x

 2  x 

S  A cos   t       A cos   t     
  u

 T  u

 t

  t x

x 
 A cos 2        A cos 2      
  T Tu 

 T  

2


 A cos  t 
x     A cos t  kx   



9. *Wave energy and wave intensity:
1
Ek  E p  VA2 2 sin 2 t  kx   
2
Density of energy:
w
Ek  E p
V

1 2 2 2
A  sin t  kx   
2
(4.25)
(4.26)
(4.27)
T
1
1
wdt  A2 2

T 0
2
Average energy in a period:
E
Wave intensity:
I  wu 
1 2 2
A  u
2
(4.28)
(4.29)
10. Huygens’ principle:
Every point of a wave front may be considered the source of secondary wavelets,
which spread out in all directions with a speed equal to the speed of propagation
of the waves.
11. Superposition principle of waves:
Several waves from different sources can propagate in the same medium
independently but at the meeting point, the resultant vibration of the particle is
the vectorial superposition of the vibrations of all waves.
12. Interference of waves:
 s1  A1 cost  kx1  1 

s2  A2 cost  kx2   2 
159
(1) Interference conditions:
Two coherent waves should have the same frequency, the same vibrational
direction and the same initial phase or constant phase change.
(2) Resultant amplitude and phase changes:
A12  A22  2 A1 A2 cos1   2 
A
(4.30)
   1   2  1   2  k x1  x2 
 1   2 
2

(a)    2m
(m  0,1,2,...)
(b)    2m  1
(c) 1  2
(4.31)
x1  x2 

(m  0,1,2,...)
  
   x1  x2  m
  x1  x2  2m  1
2
 A  A1  A2
(4.32)
 A  A1  A2
(4.33)
x1  x2   2 

(4.34)
 A  A1  A2
(4.35)
(m  0,1,2,...)  A  A1  A2
(4.36)

(m  0,1,2,...)

2
13* Standing waves:
s  s1  s2  Acost  kx  Acost  kx  2 Acos kx  cost
(a) Nodes: cos kxm  0 ,

xm  2m  1
(b) Loops: cos kxm  1 ,

xm   m 

2

4
(4.37)
(4.38)
(4.39)
14. Sound waves:
(1)* Sound pressure:
(2)* Acoustic impedance:
(3)* Sound intensity:
(4).
Intensity level:
L  10 lg
I
(dB)
I0
(4.40)
where I0 = 10-12Wm-2 is the standard reference sound intensity. Please note
that for the noises made by car on the street, the intensity made by several cars
should be the intensity of one car multiplying the number of cars. Substituting the
resultant intensity into the above formula, you will get the intensity level made by
many cars. Look at the examples given in your English text book on page 89.
15. Doppler effect
160
f observer 
vsound  vobserver
 f source
vsound  vsource
(4.41)
Besides remembering the above formula, there is still one thing you should learn
by heart. Whenever the observer and wave source move closer, plus sign will be
taken in numerator and minus sign will be taken in denominator in the above
formula. Therefore, the frequency becomes higher to the observer. On the other
hand, when they move apart, the minus and plus signs should be taken in
numerator and denominator respectively in the above formula. So the receiver get
a lower frequency.
16*. Ultrasound and its applications to medicine:
(1) Properties of ultrasonic wave
(a) Directionality, (b) High transmission, (c) Reflection.
(2) Special actions of ultrasonic wave
(a) Mechanical action, (b) Cavitation, (c) Heat effect
(3) Application of ultrasound in medicine
(a) A-ultrasound diagnosing instrument.
(b) B- ultrasound diagnosing instrument.
(c) M-ultrasound;
(d) Ultrasonic Doppler diagnosing instrument;
(e) Color Doppler ultrasonic blood-flow imaging instrument.
Chapter 5. Special relativity and General relativity
In this chapter, you should understand that the difference between Galileo
transformation and Lorentz transformation, two basic postulates, time dilation,
Lorentz contraction, the relativity of simultaneity (同时的相对性), the mass-speed
relation, the mass-energy relation, the energy-momentum relation, the two hypotheses
of general relativity, the characteristic of time-space in the gravitational force field
（引力场的时空特性）.
Important concepts and formulae:
1. The difference between the Galileo and Lorentz transformation:
(a) Galileo transformation describes the classical Newton’s mechanics. It
represents the relative principles of the classical mechanics and the absolute
outlook of time and space. Its obvious feature is that the space and time are
completely independent.
(b) Lorentz transformation agrees with the two postulates of special relativity.
The time and space are not independent any more. This transformation is the
mathematical expression of special relativity. All the phenomena,
kinematical and mechanical, happened for objects with high speed can be
explained by such a transformation.
161
 x    ( x  ut )

y  y


z  z

u 

t     t  2 x 
 c 

With  
1
1 u2 c2
(6.1)
. Using the following relation:
1 u2 c2
ds 
ds ds dt
dt
 v ,
 
 v
 v
,
u
dt 
dt  dt dt 
dt 
1  2 vx
c
we have the velocity relations:


v u
v x  x

u

1  2 vx
c

vy

(6.2)
1 u2 c2
v y 
u

1  2 vx

c
vz

1 u2 c2
v z 
u

1  2 vx
c

2. Postulates of special relativity:
(a) The relativity principle: All the laws of physics have the same form in
inertial reference frame.
(b) Constancy of the speed of light: Light propagates through empty space with
a definite speed c independent of the source or observer.
3. Time dilation, Lorentz contraction and the relativity of simultaneity:
(a) Moving clock is measured to run slowly.
   0 ,
(6.3)
where 0 is proper time and  is called the time expansion factor.
(b) Moving ruler becomes shorter.
L
1

L0 ,
(6.4)
where L0 is proper length and 1/ is called length contraction factor.
(c) The relativity of simultaneity: (t1 = t2)
x x
u
u 

 
t 2  t1    t 2  2 x 2     t1  2 x1     u  1 2 2
c
c
c

 

4. Mass-speed, mass-energy and energy-momentum relations:
162
(6.5)
(a) Mass-speed relation:
m
(b) Mass-energy relation:
E
(c) Energy-momentum relation:
While m0 = 0, we have
(d) kinetic energy
m0
1 u2 c2
m0 c 2
1 u c
2
2
 m0
(6.6)
 m0 c 2  E0
(6.7)
E 2  p 2 c 2  m02 c 4
(6.8)
E  pc
(6.9)
E k  mc 2  m0 c 2
(6.10)
5. The two hypotheses of general relativity:
(a) Equivalent principle: For all physical process, the reference frame with
uniform acceleration is equivalent to the local region of gravitation and the
inertial force is equivalent to the local region of gravitation.
(b) General relativity principle: Physics law has the same form in all reference
frames, no matter inertial or non-inertial.
6. The characteristic of time-space in the gravitational force field: In the general
theory of relativity of 1915, Einstein extended his earlier work to include
accelerated system, which led to his analysis of gravitation. He interpreted the
universe in terms of a four-dimensional space-time continuum in which the
presence of mass curves space in such a way that the gravitational field is created.
This explains that the mass curves space or the presence of gravitational field will
also curve space.
Chapter 6. The surface phenomenon of liquid
In this chapter, you need to understand the concepts of surface tension and
surface energy, and to know the concepts of the additional pressure of a curved
surface, capillarity and air embolism.
Important concepts and formulae:
1. Surface tension: Total forces pointing to the inner liquid act on molecules in the
surface layer. So the surface is in tension. It is called surface tension.
2. Surface energy: The work done by increasing liquid surface per unit area is called
surface energy. (Jm-2) Its value is equal to the surface tension coefficient
F

.
(5.1)
2L
Where F is the applied force and L is the width of the metal frame.
3. The additional pressure caused by a curved surface:
2T 2
p

For a spherical elastic pellicle:
(5.2)
R
R
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4. Capillarity:
The tube with very small diameter is called a capillary tube. When such a tube is
put into liquid, the liquid surface in it will change. The phenomenon is called
Capillarity. The level change of the liquid surface can be expressed by
h
2 cos
,
rg
(5.3)
where h is the height of liquid surface in tube, r is the radius of the tube,  is the
contact angle between the liquid and tube wall,  is the surface tension
coefficient and  is the density of liquid.
5. Air embolism:
When fluid flows in a capillary tube, liquid will be blocked if there are air
bubbles in the tube. This phenomenon is called air embolism. Because of this,
when we transfuse patients, we have to avoid air embolism in the transfusing tube.
Especially, we have to avoid an air embolism in the syringe (注射器) when
injecting veins.
Chapter 7. Ray (or geometric) optics
In this chapter, you have to know the imaging principles of a single spherical
surface, the calculation methods and sign rules; to understand the imaging principles
of the coaxial spherical system and thin lens, and their formulas; to master the optical
system of human eyes, know how to calculate the lens power for remedying sight
problem.
Important concepts and formulae:
1. The laws of reflection and refraction and total reflection:
(a) The law of reflection:
Incident angle = reflected angle
(b) The law of refraction:
(c) The total reflection angle:
n1 sin i1  n2 sin i2
sin ic 
n2
n1
(7.1)
(7.2)
2. Refraction equation of a single spherical surface:
n1 n2 n2  n1


u
v
r
(7.3)
3. Sign rules:
(a)
Object distance (物距): If the direction from object to spherical surface
is same as the direction of light, the object distance u is positive.
Otherwise it is negative. (实物物距为正,虚物物距为负).
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(b)
Image distance: If the direction from spherical surface to image is the
same as the direction of light, the image distance is positive. Otherwise it
is negative. (实像像距为正,虚像像距为负).
(c)
Curvature radius: If the direction from spherical surface to its center
point is the same as the direction of light, the curvature radius is positive.
Otherwise it is negative.
4. The thin lens equation and the lens power:
(a) The thin lens equation:
1 1 1
 
u v f
(b) The lens power:
D
(7.4)
1
(1/m)
f
(7.5)
1
AngularSiz e
(7.6)
5. *The vision of the human eyes:
vision 
Angular 
where
ObjectSize
ObjectDist ance
(minute )
6. Corrective eyeglasses for visual defects
(a) Correction of myopia;
(b) Correction of hypermetropia. (Read the examples in English textbook on
page 152-153)
7. *Magnifying glasses, fibro-scope and microscope:
Chapter 8. Wave optics
In this chapter, the important concepts are the interference and diffraction of light,
double-slit interference, thin film interference, single slit diffraction, diffractions
grating and so on.
Important concepts and formulae:
1. Interference conditions: of light:
Interference conditions: they are the same with the coherent waves. Coherent
light should also have the same frequency, the same vibrational direction and the
constant phase change.
2. Double –slit interference (Yong’s experiments):
(1) Constructive condition
 =  m
(8.1)
m
xm  
L
or
(m = 1, 2, …)
(8.2)
d
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where  is the light path difference; xm is the distance from the mth-order
bright fringe to the zeroth-order bright fringe; d is the slits separation; L
is the distance from the double-slit to the screen;  is the wavelength of
light used in the experiment.
(2) Destructive conditions:


or
1
2
    m  
(8.3)
1

x m   m   L
2 d

(8.4)
(3) Spacing of two bright fringes
(n  1)
n   L
x  x n 1  x n 
L

(8.5)
d
d
d
2. Lloyd mirror:
(1) Lloyd mirror experiment proved the abrupt phase () change on the boundary
of two mediums;
(2) The abrupt phase change occurs when the light wave initially traveling in a
less optically dense medium is reflected at an interface with a more optically
dense medium.
3. *Interference in thin films, air wedges and Newton’s ring.
4. The Fraunhofer single slit diffraction:
(1) Dark fringe positions:
m
sin  m  
(m =1, 2, 3, …)
(8.6)
a
m
xm 
f
(m =1, 2, 3, …)
(8.7)
a
where a is the width of slit, xm is the height from mth order dark fringe to the
center bright fringe, f is the focal length of the lens used in the experiment.
(2) Bright fringe positions:
1

a sin  m   m  
2

(m =1, 2, 3, …)
(8.8)
(m =1, 2, 3, …)
(8.9)
(3) The dark fringe height from
5. The diffraction grating:
Bright fringe condition:
d sin  m  m
where d is the grating spacing or grating constant.
Chapter 9. Introduction to Quantum Mechanics
In this chapter, the important concepts are the blackbody radiation, Planck’s
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hypothesis, Planck-Einstein quantization law, photoelectric effect, Compton effect,
the wave-particle duality of light, energy quantization in atoms, De Broglie wave, the
Heisenberg uncertainty principle
Important concepts and formulae
1. Blackbody radiation:
(1) Blackbody: it is defined that it can absorb all electromagnetic radiations
fallen on it;
(2) Planck’s hypotheses;
(3) Planck-Einstein quantization law:
hc
E  h 
(9.1)

2. Photoelectric effect equation.
1 2
h  W0  mvmax
(9.2)
2
3. Compton effect:
    2
h
 
sin 2  
mc
2
(9.3)
4. De Broglie Wave
p
h

5. Line spectrum and energy quantization in atoms.
(1) General Balmer series:
1 
 1
 R 2  2 

n 
k
1
(k = 1, 2, …; n = k +1, k+2, …)
(9.4)
(9.5)
(2) Bohr’s atomic theory
(1) Quantization condition of orbital angular momentum
h
2
(2) Transition postulate:
mvrn  n
(n = 1, 2, …)
h  En  Ek
(9.6)
(9.7)
(3) Important result:
Using the quantization condition of orbital angular momentum and
Newton’s law and Coulomb’s law; the energy of the atomic system
could be obtained.
En  
me 4
1
13.6
 2 E1   2 eV
2 2 2
8 0 h n
n
n
 h2
rn  0 2 n 2  r1 n 2  5.3  10 11  n 2 (m)
me
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(9.8)
6. Heisenberg uncertainty principle
h
(9.9)
p x  x 
2
7. Schrödinger equation:
(1) The interpretation of wave functions: it is probability wave function. The
function must have three properties: single value, continuous, and limited. In
addition to these conditions, it could also be normalized.
(2) Schrödinger equation:

i
 Hˆ 
t
Hˆ   E
h
.
2
1. One dimensional infinity potential well:
with  
 2 2n2
(1) Energies:
En 
(2) Wave function in well:
 x  
2mL2
2
 n 
sin 
x  using this function, the
L  L 
distribution of the particle in the well can be determined. For a given n, it
is easy to find the maximum position of its distribution.
2. Hydrogen-like atom:
(1) Energy quantization: the principal quantum number n:
me 4 Z 2
Z2
13.6  Z 2
E n   2 2 2  2 E1  
eV
8 0 h n
n
n2
(n = 1, 2, …)
(2) Angular momentum quantization: angular quantum number l:
h
L  l (l  1)
(l = 0. 1, 2, …, (n – 1))
2
(3) Space quantization: Magnetic quantum number m:
Lz  m
( m = 0, 1, 2, …, l )
(4) Spin quantization:
LS  s(s  1) ,
Lsz  ms 
(ms = -s, -s +1, …, s)
n 1
(5) Total number of states:
Z n   2(2l  1)  2n 2
l 0
Chapter 10～12
Laser, X-rays, Nuclear Physics and radioactivity
1. Laser:
(1) Absorption, spontaneous emission
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(2) Population inversion
(3) Stimulated emission.
(4) The characteristic of laser:
(a) Good directionality;
(b) High brightness and high intensity;
(c) Monochromatic;
(d) Spatially coherent;
(e) Good polarization;
2. X-rays:
(1) The characteristic of x-rays:
(a) The hardness of x-rays: The hardness of x-rays denotes the ability of
penetration of x-rays. It depends on the energy of x-photon (the
wavelength of x-rays) only and has nothing to do with the number of
x-photons.
(b) Ionizing function : x-ray enables the atoms and molecules to be ionized
and this characteristic is quite useful in medical treatment.
(c) Fluorescence function, photo-chemistry function, biological effect and
penetration capability.
3. Nuclear physics and radioactivity:
(1) The structures of nucleus:
(a) The atomic mass number A;
(b) Atomic number Z, which is the number of proton in an atom;
(c) Number of neutrons N; A = Z + N;
(d) Symbol:
A
Z
X
(2) Nuclear forces and nuclear energy levels
(3) Nuclear binding energy and mass defect
(4) The decay type of the atomic nucleus:
(a)  decay:
A
Z
X  ZA22Y  24   Q
A
Z
X  Z A1Y       Q
- decay
A
Z
X  Z A1Y       Q
+ decay
A
Z
X     Z A1Y    Q
electron capture
(b)  decay:
(5)  decay and inner transmission: In this process, a  photon is emitted.
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