SQA Databook for HN Physics
For use in Higher National Courses
Publication date: 2016
Publication code: CB7127
ISBN: 978 1 910180 10 5
Published by the Scottish Qualifications Authority
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Page two
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 three
Relationships for Physics 1
v=
1
s
t
RT
1
R1
+
1
R2
+ ........
R1
R
= 3
R2
R4
v = fλ
1
τ=
f
sin θc =
n=
=
A=
D=
R1
×V
( R1 = R2 ) S
P=
E
t
1
n
sin θ1 λ1 v1
= =
sin θ2 λ2 v2
P=
V1 =
P = IV = I 2 R =
1
f
N
t
E
m
V2
R
I
N s Vs
=
= p
N p Vp
Is
Cost = unit cost
(∑ Pt)
Random uncertainties =
H = Dwr
H
H =
t
V = IR
∑ E = ∑ IR
RT = R1 + R2 + .....
Page four
max value – min value
number of values
Relationships for Physics 2
v=
s
t
P = ρgh
Ew = Fd
v = fλ
τ=
1
1
2
Ek = mv 2
f
E p = mgh
nλ = path difference
( n + 1 / 2 ) λ = path difference
ρ1 A1 v1 = ρ2 A2 v2
1
2
P + ρgh + ρv 2 = constant
d sin θ = nλ
Q = Av
n=
sin θ1
sin θ2
Tmix =
E = hf
E = hf − hf o
hf = E1 − E2
I = Nhf = N Ahf
ρ=
m
V
F
P=
A
(T1m1 + T2m2 )
(m1 + m2 )
PV = nRT
PV = N AkaT
 ∆T 
Q = kA 
 x 
Eh = cm Δ T
Eh = lV m Eh = l f m
H = AeσT 4
Page five
Waves & Light
v=
s
t
P=
τ=
f
y = A sin ( kθ − wt )
v = fλ
λ=
1
c
f
Vd =
1
V=
f
nλ = path difference
nd − 1
n f − nc
I max − I min
× 100
I max + I min
tan θ =
y
D
tan θ =
nb
na
( n + 1 / 2 ) λ = path difference
d sin θ = nλ
n=
sin θ1 λ1 v1
= =
sin θ2 λ2 v2
sin θc =
Ep =
1
n
nλ = no +
∫ cos(kr − αx) dA
aperture
A⎛ B
⎞
+ ......... ⎟
2 ⎜ 2
λ ⎝λ
⎠
E = hf
E = hf − hf o
hf = E1 − E2
I = Nhf
w2 − w1 = hf
Page six
Electricity
V = IR
B=
∑ E = ∑ IR
F = I l B sin θ
RT = R1 + R2 + .....
1
RT
=
1
R1
+
1
R2
Xc =
X=
R1
×V
( R1 = R2 ) S
F
Q
g=
f
m
F=
2π f C
dI
dt
1
2
E = LI 2
1
2
1
2
E = QV = CV 2
P = IV = I 2 R =
E=
1
ε=− L
E
t
P=
V
I
+ ........
R1
R
= 3
R2
R4
V1 =
μ0 I
2π r
V2
R
XL =
V
I
X L = 2π f L
1 ⎛ Q1 Q2 ⎞
⎜
⎟
4 πε ⎝ r 2 ⎠
E=
Q
4 πε0 r 2
V=
Q
4 πε0 r
Ew = qV
Page seven
Radiation
Gas & Heat
A=
N
t
Tmix =
D=
E
m
PV = nRT
PV = NkaT
H = Dwr
Eh = cm Δ T
H
H =
t
N ( n) = NAe
(T1m1 + T2m2 )
(m1 + m2 )
Eh = lV m Eh = l f m
− En
kT
Δ l = α l1 (T2 − T1 )
I =σT 4
λmax =
Page eight
2 . 8978 × 10 −3
T
Mechanics
v=
s
Δt
Ew = Fd
(v − u )
a=
t
1
2
Ek = mv 2
E p = mgh
F = ma
ρ1 A1 v1 = ρ2 A2 v2
W = mg
1
2
P + ρgh + ρv 2 = constant
ω=
α=
θ
t
γ=
f
d
v=
π ρ r4
8 ηl
σ=
F
A
ε=
Δl
lo
(ω2 − ω1 )
t
s = rθ
v = rα
a=rα
I = md 2
I = Mk
2
E=
IT = Iα = Mk 2α
ρ=
m
V
p=
F
A
p = ρgh
Page nine
Fl
Ae
Quantum Mechanics
Δ to
Δt =
1−
l = l0 1 −
E = hf =
v2
c2
p=
v
c2
2
u2
1− 2
c
y ' = y;
E hf
h
=
=
c
c
λ
Δ x Δ px ≥
x − ut
x '=
hc
λ
ΔtΔE ≥
z '= z
ux
c2
t' =
u2
1− 2
c
==
=
(Position and momentum)
2
=
(energy and time)
2
h
2π
t−
−
Ψ ( x, t ) = Ψ ( x ) e
v −u
v '= x
uv
1 − 2x
c
vx =
δ Ψ ( x, t )
= 2 d 2Ψ( x)
+ U ( x ) ψ ( x, t ) = i=
2
2m dx
δt
−
v'x +u
uv′
1 + 2x
c
2
h2 d Ψ ( x )
+U ( x ) Ψ ( x ) = EΨ ( x )
2m dx 2
Pn2 n 2 h2 n 2π 2 = 2
En =
=
=
(n = 1, 2, 3 ...)
2m 8mL2 2mL2
f=
c+u
fo
c−u
Ψn ( x ) =
f=
c−u
fo
c+u
E = K + mc =
1−
K=
2
mc 2
v2
c2
1−
v2
c2
mc 2
1−
λ=
⎛ nπx ⎞
sin ⎜
⎟ (n = 1, 2, 3,...)
L
⎝ L ⎠
2
G
mv
G
p=
− iEt
h
v2
c2
h h
=
p mv
(
)
E 2 = mc 2 + ( pc )
− mc 2
2
2
E = mc 2
∫
∞
−∞
Ψ ( x ) dx = 1
T = Ge −2kL
Page ten
2
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
1
Permeability of free space
4 πЄ o
µo
8·987 × 109 N m2 C−2
4π × 10−7 N A−2
Page eleven
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
–
V
3
−1
n = 0·0224 m mol
Common Physical Quantities
Quantity
Symbol
Value
Quantity
Symbol
Value
Speed of light in vacuum
c
3·00 × 108 m s−1
Mass 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 twelve
DATA SHEET (continued)
Spectra Lines
Element
Hydrogen
Sodium
Wavelength
nm
Colour
656
Red
486
Element
Cadmium
Wavelength
nm
644
Red
Blue-green
509
Green
434
Blue-violet
480
Blue
410
Violet
397
Ultraviolet
Element
389
Ultraviolet
Carbon dioxide
589
Yellow
Lasers
Helium-neon
Wavelength
nm
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
  14
  20
Air
Hydrogen
Infrared
10590
Infrared
  633
Red
1·29
9·00 × 10−2
The gas densities refer to a temperature of 273 K and a pressure of 1·01 × 105 Pa
Page thirteen
Colour
 9550
Properties Of Selected Materials
Substance
Colour
Additional Relationships
Circle
Table of standard derivatives
circumference = 2 π r
f (x)
f ′(x)
area = π r 2
sin ax
a cos ax
cos ax
− a sin ax
Sphere
area = 4 π r 2
volume = 43 π r 3
Trigonometry
sin θ =
cos θ =
tan θ =
opposite
hypotenuse
Table of standard integrals
f (x)
sin ax
cos ax
adjacent
hypotenuse
opposite
adjacent
sin 2 θ + cos2 θ = 1
Moment of inertia
point mass
I = mr 2
rod about centre
I = 121 ml 2
rod about end
I = 31 ml 2
disc about centre
I = 21 mr 2
sphere about centre
I = 52 mr 2
Page fourteen
∫ f (x)dx
1
− cos ax + C
a
1
a
sin ax + C
Group 1
(1)
Group 2
Key
Electron Arrangements of Elements
Atomic number
1
H
Symbol
Group 0
Hydrogen
Be
4
(2)
Cr
24
2,8,13,2
Mn
25
2,8,14,2
Fe
26
2,8,15,2
Co
27
2,8,16,2
Ni
28
Copper
2,8,18,1
Cu
29
48
Zinc
2,8,18,2
Zn
30
(12)
49
Gallium
2,8,18,3
Ga
31
Aluminium
2,8,3
Al
13
Boron
2,3
B
5
(13)
50
Germanium
2,8,18,4
Ge
32
Silicon
2,8,4
Si
14
Carbon
2,4
C
6
(14)
51
Arsenic
2,8,18,5
As
33
Phosphorus
2,8,5
P
15
Nitrogen
2,5
N
7
(15)
52
Selenium
2,8,18,6
Se
34
Sulfur
2,8,6
S
16
Oxygen
2,6
O
8
(16)
53
Bromine
2,8,18,7
Br
35
Chlorine
2,8,7
Cl
17
Fluorine
2,7
F
9
(17)
54
Krypton
2,8,18,8
Kr
36
Argon
2,8,8
Ar
18
Neon
2,8
Ne
10
Group 7
3
2,2
23
2,8,13,1
Nickel
47
Group 6
Li
Beryllium
V
Cobalt
46
Group 5
2,1
12
22
2,8,11,2
45
Group 4
Lithium
Mg
Ti
Iron
Rh
Group 3
(18)
2
11
2,8,2
21
2,8,10,2
44
2
He
Na
Magnesium
Sc
Manganese
Ru
(5)
Name
(6)
(8)
Transition Elements
(7)
Nb
Sb
Te
Xe
Sn
Helium
2,8,1
20
2,8,9,2
Chromium
43
Electron arrangement
Sodium
Ca
Vanadium
Tc
(11)
19
2,8,8,2
Titanium
42
(10)
K
Scandium
Mo
(9)
2,8,8,1
Calcium
41
(4)
1
(3)
Potassium
40
Zr
I
Y
39
In
38
Cd
Sr
Ag
37
Pd
Rb
71
2,8,18,
18,8
86
Xenon
Lu
2,8,18,
18,7
Iodine
Po
70
Meitnerium Darmstadtium Roentgenium Copernicium
2,8,18,32, 2,8,18,32, 2,8,18,32, 2,8,18,32, 2,8,18,32, 2,8,18,32, 2,8,18,32, 2,8,18,32, 2,8,18,32, 2,8,18,32,
18,9,2
32,10,2
32,11,2
32,12,2
32,13,2
32,14,2
32,15,2
32,17,1
32,18,1
32,18,2
Rn
Polonium
Yb
2,8,18,
18,6
Tellurium
85
Bi
69
At
Bismuth
Tm
2,8,18,
18,5
Antimony
84
68
2,8,18,
18,4
Tin
83
Er
Pb
67
2,8,18,
18,3
Tl
Ho
2,8,18,
18,2
Hg
66
Au
Dy
2,8,18,
18,1
Pt
65
2,8,18,
18,0
Ir
77
2,8,18,13, 2,8,18,13, 2,8,18,15, 2,8,18,16,
1
2
1
1
76
Tb
2,8,18,
12,1
Os
64
2,8,18,
10,2
75
Gd
Radon
2,8,18,
32,18,8
63
Ce
Thulium
Ytterbium
Lutetium
Terbium
Erbium
Gadolinium
Holmium
Europium
98
Dysprosium
Samarium
Cf
Praseodymium Neodymium Promethium
97
2,8,18,21, 2,8,18,22, 2,8,18,23, 2,8,18,24, 2,8,18,25, 2,8,18,25, 2,8,18,27, 2,8,18,28, 2,8,18,29, 2,8,18,30, 2,8,18,31, 2,8,18,32, 2,8,18,32,
8,2
8,2
8,2
8,2
8,2
9,2
8,2
8,2
8,2
8,2
8,2
8,2
9,2
Astatine
Eu
2,8,18,9,2
Re
2,8,18,8,1 2,8,18,8,2
74
Indium
Niobium
W
Cadmium
73
2,8,18,
32,18,7
Silver
Zirconium
Ta
Palladium
Yttrium
72
2,8,18,
32,18,6
Hs
62
La
Cerium
Bk
Lr
96
103
Cm
No
95
102
Am
101
94
Md
Pu
100
93
Fm
Np
99
U
92
Es
91
90
Pa
Th
Berkelium
89
Curium
Ac
Lanthanum
Lead
Hassium
Sm
2,8,18,32, 2,8,18,32, 2,8,18,32, 2,8,18,32, 2,8,18,32,
12,2
13,2
14,2
15,2
17,1
Bh
61
2,8,18,18, 2,8,18,32,
9,2
10,2
Rhodium
Strontium
Hf
Thallium
2,8,18,18, 2,8,18,18,
8,1
8,2
Bohrium
Pm
Cn
Sg
60
Rg
Db
Seaborgium
Nd
Ds
Rf
Dubnium
59
Mt
Ac
Rutherfordium
Pr
Molybdenum Technetium Ruthenium
Rubidium
57
112
Mercury
82
La
111
Gold
81
56
110
Platinum
80
Ba
109
Iridium
79
55
108
Osmium
78
Cs
107
Rhenium
2,8,18,
32,18,5
106
Tungsten
2,8,18,
32,18,4
105
Tantalum
2,8,18,
32,18,3
104
Hafnium
2,8,18,
32,18,2
89
Lanthanum
2,8,18,
32,18,1
88
Barium
Ra
Actinium
58
2,8,18,
32,11,2
87
Caesium
Fr
Radium
2,8,18,32, 2,8,18,32,
18,8,1
18,8,2
57
2,8,18,
20,8,2
Lanthanides
Francium
2,8,18,
18,9,2
Actinides
Americium
Mendelevium
Plutonium
Fermium
Neptunium
Protactinium
Uranium
Thorium
Californium Einsteinium
Nobelium
Lawrencium
2,8,18,32, 2,8,18,32, 2,8,18,32, 2,8,18,32, 2,8,18,32, 2,8,18,32, 2,8,18,32, 2,8,18,32, 2,8,18,32, 2,8,18,32, 2,8,18,32, 2,8,18,32, 2,8,18,32, 2,8,18,32, 2,8,18,32,
18,9,2
18,10,2
20,9,2
21,9,2
22,9,2
24,8,2
25,8,2
25,9,2
27,8,2
28,8,2
29,8,2
30,8,2
31,8,2
32,8,2
32,9,2
Actinium
Page fifteen