HARD EQUATIONS

Question 1

beer-lambert law

Answer 1

E = A/cl

Question 2

number of unpaired electrons

Answer 2

n=✔️(u^2+1)-1

Question 3

magnetic moment for spin only systems

Answer 3

u=2✔️S(S+1)

Question 4

magnetic moment when we know n

Answer 4

u=✔️n(n+2)

Question 5

Lennard jones equation

Answer 5

V(R)=4E[sigma^12/R^12 - sigma^6/R^6]

Question 6

what is each term in the Lennard jones equation

Answer 6

V(R) = function of potential energy
E = min potential energy of interaction
R = distance between unknown but identical atoms
sigma = molecular separation when V(R) =0

Question 7

vapour pressure

Answer 7

p = Δm/AΔt . ✔️(2piRT/M)

Question 8

force =

Answer 8

Δp/Δt

Question 9

pressure =

Answer 9

F/A

Question 10

ZA =

Answer 10

✔️2 . simga . <s-> . (p/KbT)</s->

Question 11

lamda(distance between collisions) =

Answer 11

mean speed / ZA

Question 12

t (time between collisions) =

Answer 12

1/ZA

Question 13

sigma =

Answer 13

pi d^2

Question 14

A =

Answer 14

NA . (sigma.<s->/✔️2)</s->

Question 15

rate of effusion =

Answer 15

pANA / ✔️(2.pi.M.R.T)

Question 16

real gas equation =

Answer 16

p = (RT/Vm-b) - (a/Vm^2)

Question 17

rate of effusion is proportional to

Answer 17

1/✔️m . T

Question 18

total energy of an electron =

Answer 18

Ecoul + Ek

Question 19

lamda (spectroscopy) =

Answer 19

h/mV

Question 20

radius of Bohr model =

Answer 20

r.n = n.h/m.V

Question 21

Rydberg equation (from Bohr model) =

Answer 21

E = Rh . Z^2eff [1/ni^2 - 1/nf^2]

Question 22

volume of sphere

Answer 22

4/3 pir^3

Question 23

madelung equation

Answer 23

-e^2NA / 4pi E0 r [6 - 12/✔️2 + 8/✔️3]

Question 24

packing efficiency of 2D

Answer 24

area occupied by circles / area of unit cells

Question 25

packing efficiency of 3D

Answer 25

number of atoms in unit cell x volume of atoms / total volume of unit cell

Question 26

a in terms of r for prim

Answer 26

a = 2r

Question 27

volume of prim unit cell

Answer 27

a^3 = (2r)^3 = 8r^3

Question 28

a in terms of r for BCC

Answer 28

a = 4r/✔️3

Question 29

volume of BCC unit cell

Answer 29

a^3 = (4r/✔️3)^3 = 64r^3 / 3✔️3

Question 30

p (density) =

Answer 30

m/V

Question 31

P(density)(longer) =

Answer 31

p = n.M/V.NA

Question 32

magnetic flux density =

Answer 32

Fmag = q.v.B (velocity)(B= magnetic flux density)

Question 33

lorentz force law

Answer 33

F = qE + qvB

Question 34

Curie-weiss behaviour

Answer 34

Xm = c/T-sigma (Xm is the molar susceptibility)

Question 35

ohms law

Answer 35

R = V/I

Question 36

conductivity

Answer 36

sigma = 1/P

Question 37

refractive index

Answer 37

n = c/v (c is velocity of light in vacuum, v is velocity of light in material)

Question 38

Reflectivity

Answer 38

R = (n2-n1/n2+n1)^2

Question 39

lambda (properties of solids) =

Answer 39

hc/Eg

Question 40

molar heat capacity

Answer 40

Q/n.ΔT

Question 41

heat flux (Fourier's Law)

Answer 41

q = -k . ΔT/L

Question 42

thermal energy Q =

Answer 42

Q = m.c.ΔT

Question 43

Wiedemann-Franz Law (thermal conductivity/electrical conductivity)

Answer 43

k/sigma = L.T

Question 44

cosine rule

Answer 44

a^2 = b^2 + c^2 - 2bccosA

Question 45

what is c, a and b in terms of r for HCP

Answer 45

a = b = 2r c = 4✔️2/3 . r

Question 46

sigma =

Answer 46

sigma0 exp (-Ea/kT)