Modern Physics
Important formulas-FAT
Module-IV (Semiconductors)
1. Current density
J=
I
A
µ=
vd
E
A is the cross sectional area.
2. Definition of mobility:
3. Conductivity of any semiconductor (intrinsic or extrinsic):
σ = enµe + epµh
4. Conductivity of an intrinsic semiconductor:
σi = eni (µe + µh )
5. Conductivity of an n-type semiconductor:
σ = enµe ≈ eNd µe
6. Conductivity of a p-type semiconductor
σ = epµh ≈ eNa µh
7. Relationship between resistivity and conductivity:
ρ=
1
σ
8. Resistance of a material of length l and cross-sectional area A:
R=ρ
l
A
9. Effective density of states in the conduction band:
3/2
2πm∗e kT
NC = 2
h2
10. Effective density of states in the valence band:
3/2
2πm∗h kT
NV = 2
h2
11. Intrinsic carrier concentration:
Eg
ni = (NC NV )1/2 e− 2kT
12. Dependence of conductivity on absolute temperature T :
Eg
σ = σo e− 2kT
13. Dependence of resistivity on absolute temperature T :
Eg
ρ = ρo e 2kT
14. If n is the concentration of electrons and p is the concentration of holes in any
semiconductor (intrinsic or extrinsic) then
n2i = np
15. Concentration or density of electrons in a semiconductor:
n = NC e−
EC −EF
kT
16. Concentration or density of holes in a semiconductor:
p = NV e−
EF −EV
kT
17. Hall voltage developed across a semiconductor:
RH IB
VH =
t
18. Hall coefficient:
1
, for n-type semiconductor
ne
1
RH = , for p-type semiconductor
pe
RH = −
19. Drift velocity of charge carriers (electrons in n-type and holes in p-type semiconductor)
VH
vd =
wB
20. Built-in barrier potential of a PN-junction diode:
Na Nd
Vbi = Vt ln 2
ni
where Vt =
kT
.
e
21. Fill factor for a solar cell:
FF =
(V I)max
VOC ISC
22. Efficiency of a solar cell:
Maximum electrical power delivered
(V I)max
η=
=
Solar power incident
Pi
23. Wavelength of emission from a LED:
λ=
hc
Eg
Module-V (Magnetic Materials)
1. Magnetic susceptibility:
−
→
M
χ= →
−
H
2. Relative permeability:
µr =
µ
µ0
3. Relationship between relative permeability and magnetic susceptibility:
µr = 1 + χ
4. Magnetic induction or magnetic flux density:
→
−
→
− −
→
B = µ0 ( H + M )
5. Magnetic moment due to a current carrying loop with N no. of turns:
→
−
µ = N IAk̂
6. Magnetic field at the centre of a circular current carrying loop with N no. of
turns:
→
−
µ0 N I
k̂
B =
2r
7. Temperature dependence of magnetic susceptibility for a paramagnetic substance:
C
χ=
T
8. Saturation magnetization of a ferromagnetic material:
Ms = xµB nat
where nat can be calculated by
nat =
ρnAv
MAt
Module- I (Interference)
1. Fringe width in Young’s double slit experiment:
β=
λD
d
2. Position of ‘n’th order bright fringe in Young’s double slit experiment:
xn =
nλD
d
3. Position of ‘n’th order dark fringe in Young’s double slit experiment:
(n + 12 )λD
xn =
d
Module- II (Diffraction)
1. Condition for ‘m’th-order diffraction minimum through a single-slit:
asinθ = mλ
Module-III (Quantum Mechanics)
1. de-Broglie wavelength for any particle with velocity ‘v’:
λ=
h
mv
2. de-Broglie wavelength of a particle having kinetic energy E:
λ= √
h
2mE
3. de-Broglie wavelength of a charge particle (with charge ‘q’) accelerated by potential difference of V volts:
h
λ= √
2mqV