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

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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