Modern Physics Unit-1 formulas only

Question 1

Stefan’s Law Formula

Answer 1

E = σT^4

Question 2

Wein’s law

Answer 2

U(underscore λ) d λ = C1 λ^-5 e^(-C2/ λT)d λ

Question 3

Planck’s Law of Radiation

Answer 3

U(underscore λ) d λ = 8πhcλ^-5dλ[1/e^hv/KT - 1]

Question 3

lord Rayleigh jeans law

Answer 3

U(underscore λ) d λ = 8πkTλ^-4dλ

Question 4

relation between energy and frequency of radiations

Answer 4

E = nhv (n=int, h= 6.625 x 10^-34 Js, v=frequency of radiations)

Question 5

The Change in Wavelength is given by

Answer 5

λ’ - λ = h(1-cosΦ)/mo C

Question 6

When the angle of scattering is 90, the Compton shift(λ’ - λ) is found to be

Answer 6

0.0243 Å.

Question 7

De-Broglie wavelength of a free particle

Answer 7

λ= h/√2mE = h/√2meV (since E = eV) where V is the accelerating potential on an electron
or λ = 12.27/√V Ǻ.

Question 8

de Broglie hypothesis

Answer 8

λ = h/p

Question 8

Momentum of a De-Broglie wavelength of a free particle

Answer 8

p=√2mE….(mass of electron= 9.1 x 10^-31, E= energy)

Question 8

Group velocity formula

Answer 8

Vg = ∂ω/∂k

Question 9

The wavelength of a particle is given by

Answer 9

λ= h/p = h/mv

Question 10

Phase velocity formula

Answer 10

p = ω/k

Question 12

Heisenberg’s uncertainty principle

Answer 12

Δp.Δx ≥h/4π
ΔE.Δt ≥ h/4π
ΔL.Δθ≥ h/4π
ΔE = uncertainty in measurement of energy
Δt = uncertainty in measurement of time
ΔL = uncertainty in measurement of angular momentum
Δθ = uncertainty in measurement of angular distance