Notes - Fisika - Radiasi

Radiasi Benda Hitam

P=e*σ*A*T^4

T, Temperature, T=(T_C)+273

(A_), Area

e, Emisivitas 0≤e≤1

σ=5.67⋅10^(-8), Boltzmann constant

Light is a wave.

c=ƒ*λ

c=3⋅10^8, the speed of light (m/s)

ƒ, Frequency (Hz)

λ, Wavelength (m)

Ex. 1

P=0.8⋅5.67⋅10^(-8)⋅(10⋅10^(-2))^2⋅(727+273)^4=2268/5=453.6

Ex. 2

32=x⋅(127+273)^4

x=1/800000000

P=1/800000000⋅(327+273)^4=162W

Ex. 3

(I_S)=1400⋅((1.5⋅10^11)/(7⋅10^8))^2=450000000/7=64285714.28

(I_S)=5.67⋅10^(-8)⋅T^4

T^4=64285714.28/(5.67⋅10^(-8))

T=5802.736551281401K

Ex. 4

E=5.67⋅10^(-8)⋅0.5⋅2⋅10^(-6)⋅100^4⋅10

E=567/10000000=567⋅10^(-7)=5.67⋅10^(-5)

Ex. 5

3.6⋅10^26=6⋅10^16⋅5.67⋅10^(-8)⋅1⋅T^4

T=√(4,(3.6⋅10^26)/(6⋅10^16⋅5.67⋅10^(-8)))=20000/21*5^3/4√(4,1029)

Wien

t⋅λ=C

The hotter a black body is, the smaller the wavelength emitted.

C=2.9⋅10^(-3), the Wien constant

T, Temperature

Plancke

E=h*ƒ=(h*c)/λ

E, Energy of a Singular Photon

h=6.6⋅10^(-34), Plancke's Constant

Compton

E=h⋅c/λ

(E^′)=h⋅c/(λ^′)

Δ(λ)=(λ^′)-λ

Δ(λ)=h/(m⋅c)⋅cos(θ)

m=9.1⋅10^(-31)

c=3⋅10^8

(E_k)=E-(E^′)=1/2*m*v^2

Problem 1

Δ(λ)=(2.43⋅10^(-12))/(9.1⋅10^(-31)⋅3⋅10^8)⋅1/2=0,0012

λ=0.2-0.0012=0.1988

Problem 2

λ=0.035mm=3.5⋅10^(-11)

θ=37°

Δ(λ)=(6.6⋅10^(-34))/(9.1⋅10^(-31)⋅3⋅10^8)⋅(1-4/5)
=4.835⋅10^(-13)

(λ^′)=4.835⋅10^(-13)+3.5⋅10^(-11)=3.54⋅10^(-11)

(E^′)=6.6⋅10^(-34)⋅(3⋅10^8)/(3.54⋅10^(-11))=5.59⋅10^(-15)

(E_k)=6.6⋅10^(-34)⋅(3⋅10^8)/(3.5⋅10^(-11))-5.59⋅10^(-15)=6.71⋅10^(-17)

Problem 3

λ=1⋅10^(-10)

θ=90°

∴Δ(λ)=(6.6⋅10^(-34))/(9.1⋅10^(-31)⋅3⋅10^8)⋅(1-cos(90°))=2.42⋅10^(-12)

(λ^′)=2.42⋅10^(-12)+1⋅10^(-10)=1.02⋅10^(-10)

(E_k)=6.6⋅10^(-34)⋅3⋅10^(-8)⋅(1/(1⋅10^(-10))-1/(1.02⋅10^(-10)))=3.88⋅10^(-33)

3.88⋅10^(-33)=1/2⋅