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transcript
SQA Databook for HN Physics
For use in Higher National Courses
Publication date: 2016Publication code: CB7127ISBN: 978 1 910180 10 5
Published by the Scottish Qualifications AuthorityThe Optima Building, 58 Robertson Street, Glasgow G2 8DQLowden, 24 Wester Shawfair, Dalkeith, Midlothian EH22 1FD
www.sqa.org.uk
The information in this publication may be reproduced in support of SQA qualifications. If it is reproduced, SQA should be clearly acknowledged as
the source. If it is to be used for any other purpose, then written permission must be obtained from SQA. It must not be reproduced for
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© Scottish Qualifications Authority 2016
Page two
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Page three
Contents
Relationships for Physics 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Relationships for Physics 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Waves & Light. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Electricity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Radiation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Gas & Heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Quantum Mechanics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10
Fundamental Physics Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11
DATA SHEET
Standard Pressure and Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12
Common Physical Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12
Refractive Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12
Spectra Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13
Properties of Selected Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13
Additional Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14
Electron Arrangements of Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15
Page four
Relationships for Physics 1
svt
=
v fλ=
1τf
=
sin 1cθ n=
sinsin
1 1 1
2 2 2
θ λ vnθ λ v
= = =
1Pf
=
NAt
=
EDm
=
rH Dw=
HHt
=
V IR=
E IR=∑∑
.....1 2TR R R= + +
........1 2
1 1 1
TR R R= + +
1 3
2 4
R RR R
=
( )1
11 2
SRV V
R R= ×
=
EPt
=
22 VP IV I R
R= = =
ps s
p p s
IN VN V I
= =
Cost unit cost Pt = ( )∑
–max value min valueRandom uncertainties
number of values=
Page five
Relationships for Physics 2
svt
=
v fλ=
1τf
=
nλ path difference=
( )/1 2n λ path difference+ =
sind θ nλ=
sinsin
1
2
θnθ
=
E hf=
oE hf hf= −
1 2hf E E= −
AI Nhf N hf= =
mρV
=
FPA
=
P ρgh=
wE Fd=
212kE mv=
pE mgh=
1 1 1 2 2 2ρ A v ρ A v=
21constant
2P ρgh ρv+ + =
vQ A=
( )( )1 1 2 2
1 2mix
Tm T mT
m m+
=+
PV nRT=
A aPV N k T=
∆TQ kAx
=
ΔhE cm T=
h V h fE l m E l m= =
4H AeσT=
Page six
Waves & Light
svt
=
v fλ=
cλf
=
1τf
=
nλ path difference=
( )/1 2n λ path difference+ =
sind θ nλ=
sinsin
1 1 1
2 2 2
θ λ vnθ λ v
= = =
sin 1cθ n=
.........2 2oA Bnλ nλ λ⎛ ⎞= + +⎜ ⎟⎝ ⎠
E hf=
oE hf hf= −
1 2hf E E= −
I Nhf=
2 1w w hf− =
1Pf
=
( )siny A kθ wt= −
1dd
f c
nVn n
−=−
max min
max min
100I IVI I
−= ×+
tan yθD
=
tan b
a
nθn
=
cos( )paperture
E kr αx dA= −∫
Page seven
Electricity
V IR=
E IR=∑ ∑
.....1 2TR R R= + +
........1 2
1 1 1
TR R R= + +
1 3
2 4
R RR R
=
( )1
11 2
SRV V
R R= ×
=
EPt
=
22 VP IV I R
R= = =
FEQ
=
fgm
=
1 22
1
4
Q QFπε r
⎛ ⎞= ⎜ ⎟⎝ ⎠
204
QEπε r
=
04
QVπε r
=
wE qV=
0
2
μ IBπ r
=
sinF I l B θ=
cVXI
=
12
Xπ f C
=
dIε Ldt
= −
212
E LI=
21 12 2
E QV CV= =
LVXI
=
2LX π f L=
Page eight
Radiation
NAt
=
EDm
=
rH Dw=
HHt
=
( )EnkTN n NAe
−
=
Gas & Heat
( )( )1 1 2 2
1 2mix
Tm T mT
m m+
=+
PV nRT=
aPV Nk T=
ΔhE cm T=
h V h fE l m E l m= =
( )Δ 1 2 1l α l T T= −
4I σT=
max. 32 8978 10λ
T
−×=
Page nine
Mechanics
Δsvt
=
( )v ua
t−
=
F ma=
W mg=
θωt
=
( )2 1ω ωα
t−
=
s rθ=
v rα=
a r α=
2I md=
2I Mk=
2IT Iα Mk α= =
mρV
=
FpA
=
p ρgh=
wE Fd=
212kE mv=
pE mgh=
1 1 1 2 2 2ρ A v ρ A v=
21constant
2P ρgh ρv+ + =
fγd
=
4
8
π ρ rvηl
=
FσA
=
Δ
o
lεl
=
FlEAe
=
Page ten
Quantum Mechanics
ΔΔ2
21
ottvc
=−
2
0 21vl lc
= −
'2
21
x utxuc
−=−
' ; 'y y z z= =
'2
2
21
uxtctuc
−=
−
'
21
x
x
v uvuvc
−=−
'
21x
x
v x uv uvc
+= ′+
oc uf fc u
+=−
oc uf fc u
−=+
2
21
mvpvc
=−
22
2
21
mcK mcvc
= −−
h hλp mv
= =
hcE hfλ
= =
E hf hpc c λ
= = =
Δ Δ (Position and momentum)2xx p ≥
(Δ Δ energy and time)2
t E ≥
2
hπ
=
( ) ( )Ψ ,Ψ( ) ( , )2 2
22
δ x td x U x ψ x t im dx δt
− + =
( ) ( )Ψ , ΨiEthx t x e
−
=
( ) ( ) ( ) ( )ΨΨ Ψ
22
22
d xh U x x E xm dx
− + =
( , , ...)2 2 2 2 2 2
2 2 1 2 32 8 2n
nP n h n πE nm mL mL
= = = =
( )Ψ sin ( , , ,...)21 2 3n
nπxx nL L
⎛ ⎞= =⎜ ⎟⎝ ⎠
22
2
21
mcE K mcvc
= + =−
( ) ( )2 22 2E mc pc= +
2E mc=
( )Ψ 21x dx
∞
−∞=∫
2kLT Ge−=
Page eleven
Fundamental Physics Constants
Name Symbol Value
Gravitational constant G 6·67408 × 10−11 m3 kg−1 s−2
Mass of the earth ME 5·972 × 1024 kg
Radius of the earth rE 6,371 × 103 m
Planck’s constant h 6·63 × 10−34 J s
Boltzmann’s constant k 1·38066 × 10−23 J K−1
Stefan — Boltzmann constant σ 5·67 × 10−8 W m−2 K−4
Wien’s constant – 2·90 × 10−3 m K
Avogadro’s number NA 6·022 × 1023
Gas constant R 8·314510 J mol−1 K−1
Monatomic Adiabatic index – 1·67
Mass of electron me 9·10939 × 10−31 kg
Mass of neutron mn 1·67493 × 10−27 kg
Mass of proton Mp 1·67262 × 10−27 kg
Electron volt eV 1·603 × 10−19 J
Permittivity of free space εo 8·854 × 10−12 C2 N m−2
14 oπЄ 8·987 × 109 N m2 C−2
Permeability of free space µo 4π × 10−7 N A−2
Page twelve
DATA SHEET
Standard Pressure and Temperature
Quantity Symbol Value
Standard temperature T 273 K
Standard pressure P 1·013 × 105 Pa
Molar volume of an ideal gas – Vn = 0·0224 m3 mol−1
Common Physical Quantities
Quantity Symbol Value Quantity Symbol Value
Speed of light in vacuum c 3·00 × 108 m s−1Mass of electron me 9·11 × 10−31 kg
Magnitude of the charge on an electron e 1·60 × 10−19 C
Mass of neutron mn 1·675 × 10−27 kg
Gravitational acceleration on Earth g 9·81 m s−2 Mass of
proton mp 1·673 × 10−27 kg
Planck’s constant h 6·63 × 10−34 J s
Refractive Indices
The refractive indices refers to sodium light of wavelength 589 nm and to substances at a temperature of 273 K.
Substance Refractive Index
Substance Refractive Index
Diamond 2·42 Water 1·33
Crown glass 1·50 Air 1·00
Page thirteen
DATA SHEET (continued)
Spectra Lines
Element Wavelength nm
Colour Element Wavelength nm
Colour
Hydrogen
Sodium
656
486
434
410
397
389
589
Red
Blue-green
Blue-violet
Violet
Ultraviolet
Ultraviolet
Yellow
Cadmium 644
509
480
Red
Green
Blue
Lasers
Element Wavelength nm
Colour
Carbon dioxide
Helium-neon
9550
10590
633
Infrared
Infrared
Red
Properties Of Selected Materials
Substance Density kg m−3
Melting point K
Boiling point K
Aluminium 2·70 × 103 933 2623
Copper 8·96 × 103 1357 2853
Ice 9·20 × 102 273
Sea Water 1·02 × 103 264 377
Water 1·00 × 103 273 373
Air 1·29
Hydrogen 9·00 × 10−2 14 20
The gas densities refer to a temperature of 273 K and a pressure of 1·01 × 105 Pa
Page fourteen
Additional Relationships
Circle
πcircumference 2 r=
π 2area r=
Sphere
π 2area 4 r=
π 343volume r=
Trigonometry
sin oppositehypotenuse
θ =
cos adjacenthypotenuse
θ =
tan oppositeadjacent
θ =
sin cos2 2 1θ θ+ =
Moment of inertia
point mass
2I mr=
rod about centre
2112I ml=
rod about end
213I ml=
disc about centre
212I mr=
sphere about centre
225I mr=
Table of standard derivatives
f (x) f ′(x)
sin ax cosa ax
cosax sina ax−
Table of standard integrals
f (x) ∫ f (x)dx
sin ax cos1 ax Ca
− +
cosax sin1 ax Ca
+
Page fifteen
Electron Arrangem
ents of Elements
Group 1
Group 2
Group 3
Group 4
Group 5
Group 6
Group 7
Group 0
(1)(18)
1H1
Hydrogen
KeyAtom
ic number
Symbol
Electron arrangement
Nam
e
2He2
Helium
(13)(14)
(15)(16)
(17)(2)
3Li2,1
Lithium
4Be2,2
Beryllium
5B2,3
Boron
6C2,4
Carbon
7N2,5
Nitrogen
8O2,6
Oxygen
9F2,7
Fluorine
10
Ne2,8
Neon
11
Na
2,8,1
Sodium
12
Mg
2,8,2
Magnesium
Transition Elements
13Al
2,8,3
Aluminium
14Si2,8,4
Silicon
15P2,8,5
Phosphorus
16S2,8,6
Sulfur
17Cl2,8,7
Chlorine
18
Ar
2,8,8
Argon(3)
(4)(5)
(6)(7)
(8)(9)
(10)(11)
(12)
19K2,8,8,1
Potassium
20
Ca2,8,8,2
Calcium
21
Sc2,8,9,2
Scandium
22Ti2,8,10,2
Titanium
23V2,8,11,2
Vanadium
24
Cr2,8,13,1
Chromium
25
Mn
2,8,13,2
Manganese
26
Fe2,8,14,2
Iron
27
Co2,8,15,2
Cobalt
28
Ni
2,8,16,2
Nickel
29
Cu2,8,18,1
Copper
30
Zn2,8,18,2
Zinc
31
Ga
2,8,18,3
Gallium
32
Ge
2,8,18,4
Germ
anium
33
As
2,8,18,5
Arsenic
34
Se2,8,18,6
Selenium
35
Br2,8,18,7
Bromine
36
Kr2,8,18,8
Krypton
37
Rb2,8,18,8,1
Rubidium
38Sr2,8,18,8,2
Strontium
39Y2,8,18,9,2
Yttrium
40
Zr2,8,18,
10,2Zirconium
41
Nb
2,8,18,12,1
Niobium
42
Mo
2,8,18,13,1
Molybdenum
43
Tc2,8,18,13,
2Technetium
44
Ru2,8,18,15,
1Ruthenium
45
Rh2,8,18,16,
1Rhodium
46
Pd2,8,18,
18,0Palladium
47
Ag
2,8,18,18,1Silver
48
Cd2,8,18,
18,2Cadm
ium
49In2,8,18,
18,3Indium
50
Sn2,8,18,
18,4Tin
51
Sb2,8,18,
18,5Antim
ony
52
Te2,8,18,
18,6Tellurium
53I2,8,18,
18,7Iodine
54
Xe2,8,18,
18,8Xenon
55
Cs2,8,18,18,
8,1Caesium
56
Ba2,8,18,18,
8,2Barium
57
La2,8,18,18,
9,2Lanthanum
72
Hf
2,8,18,32,10,2
Hafnium
73
Ta2,8,18,32,11,2Tantalum
74W2,8,18,32,
12,2Tungsten
75
Re2,8,18,32,
13,2Rhenium
76
Os
2,8,18,32,14,2
Osm
ium
77Ir2,8,18,32,
15,2Iridium
78
Pt2,8,18,32,
17,1Platinum
79
Au
2,8,18,32,18,1
Gold
80
Hg
2,8,18,32,18,2M
ercury
81Tl2,8,18,32,18,3Thallium
82
Pb2,8,18,32,18,4
Lead
83Bi2,8,18,32,18,5Bism
uth
84
Po2,8,18,32,18,6Polonium
85
At
2,8,18,32,18,7Astatine
86
Rn2,8,18,32,18,8Radon
87
Fr2,8,18,32,
18,8,1Francium
88
Ra2,8,18,32,
18,8,2Radium
89
Ac
2,8,18,32,18,9,2
Actinium
104
Rf2,8,18,32,
32,10,2Rutherfordium
105
Db
2,8,18,32,32,11,2D
ubnium
106
Sg2,8,18,32,
32,12,2Seaborgium
107
Bh2,8,18,32,
32,13,2Bohrium
108
Hs
2,8,18,32,32,14,2H
assium
109
Mt
2,8,18,32,32,15,2
Meitnerium
110
Ds
2,8,18,32,32,17,1
Darmstadtium
111
Rg2,8,18,32,
32,18,1Roentgenium
112
Cn2,8,18,32,
32,18,2Copernicium
57
La2,8,18,18,9,2
Lanthanum
58
Ce2,8,18,20,8,2Cerium
59
Pr2,8,18,21,
8,2Praseodym
ium
60
Nd
2,8,18,22,8,2
Neodym
ium
61
Pm2,8,18,23,
8,2Prom
ethium
62
Sm2,8,18,24,
8,2Sam
arium
63
Eu2,8,18,25,
8,2Europium
64
Gd
2,8,18,25,9,2
Gadolinium
65
Tb2,8,18,27,
8,2Terbium
66
Dy
2,8,18,28,8,2
Dysprosium
67
Ho
2,8,18,29,8,2
Holm
ium
68
Er2,8,18,30,
8,2Erbium
69
Tm2,8,18,31,
8,2Thulium
70
Yb2,8,18,32,
8,2Ytterbium
71
Lu2,8,18,32,
9,2Lutetium
89
Ac
2,8,18,32,18,9,2
Actinium
90
Th2,8,18,32,
18,10,2Thorium
91
Pa2,8,18,32,
20,9,2Protactinium
92U2,8,18,32,
21,9,2U
ranium
93
Np
2,8,18,32,22,9,2
Neptunium
94
Pu2,8,18,32,
24,8,2Plutonium
95
Am
2,8,18,32,25,8,2
Americium
96
Cm2,8,18,32,
25,9,2Curium
97
Bk2,8,18,32,
27,8,2Berkelium
98
Cf2,8,18,32,
28,8,2Californium
99
Es2,8,18,32,
29,8,2Einsteinium
100
Fm2,8,18,32,
30,8,2Ferm
ium
101
Md
2,8,18,32,31,8,2
Mendelevium
102
No
2,8,18,32,32,8,2
Nobelium
103
Lr2,8,18,32,
32,9,2Law
rencium
Lanthanides
Actinides