What is the difference between planck's equation and planck's formula?

PLANCK'S EQUATION

Planck theorized that energy was not transferred as a whole, but in chunks of energy - later known as quanta, given by the equation E=hν,E=hν,

where hh is Planck’s constant and νν is the frequency of the photon.

This helped solve a lot of problems in Physics back in the day, one of most importance, being the Ultraviolet Catastrophe, which was so troublesome that a pompous name like that was assigned to the problem.

This puzzled Physicists for a while, since apparently, the radiation emitted was increasing with increasing Temperature. This was definitely not correct since the theory predicted infinite radiation emitted at very high temperatures, which was not observed in reality.

It wasn’t until Planck realized that the Rayleigh - Jeans law needed a modification. It needed an extra term that would make a cut-off threshold which would lead to the exponential drop of the curve after a certain Temperature which would then prevent the Ultraviolet catastrophe predicted by the previous theory.

The Rayleigh - Jeans law stated that:

Bν(T)=2ν2kBTc2Bν(T)=2ν2kBTc2

leading to the blue curve, while the red one was observed by experimentation and supported by common sense.

PLANCK'S FORMULA

k = 1

P(t) = (t + 20)²

Step-by-step explanation:

P' = k√P = k P⁰•⁵

To solve for k,

P' = 10 rabbits/month

P = 100 rabbits

10 = k √100

10 = 10k

k = 1

To solve for P(t)

P' = dP/dt

(dP/dt) = kP⁰•⁵

dP/P⁰•⁵ = k dt

P⁻⁰•⁵ dP = k dt

∫ P⁻⁰•⁵ dP = ∫ k dt

2P⁰•⁵ = kt + c

At t = 0, P = 100

2(100)⁰•⁵ = 0 + c

2 × 10 = c

c = 20

2P⁰•⁵ = kt + c

2P⁰•⁵ = kt + 20

Recall, k = 1

2P⁰•⁵ = t + 20

P⁰•⁵ = (t + 20)

P(t) = (t + 20)²