Question of The Day.. ^_^
Give me the Derivation of De Broglie equation.....⭐⭐
Please Don't spam❌
Content Quality required✔
Answers
Answered by
7
Heya...
De Broglie Hypothesis...
In quantum mechanics, matter is believed to behave both like a particle and a wave at the sub-microscopic level. The particle behavior of matter is obvious. When you look at a table, you think of it like a solid, stationary piece of matter with a fixed location. At this macroscopic scale, this holds true. But when we zoom into the subatomic level, things begin to get more complicated, and matter doesn't always exhibit the particle behavior that we expect.
This non-particle behavior of matter was first proposed in 1923, by Louis de Broglie, a French physicist. In his PhD thesis, he proposed that particles also have wave-like properties. Although he did not have the ability to test this hypothesis at the time, he derived an equation to prove it using Einstein's famous mass-energy relation and the Planck equation.
Deriving the de Broglie Wavelength
De Broglie derived his equation using well established theories through the following series of substitutions:
De Broglie first used Einstein's famous equation relating matter and energy:
with
E = energy,m = mass,c = speed of light
Using Planck's theory which states every quantum of a wave has a discrete amount of energy given by Planck's equation:
E=hν(1.2)(1.2)E=hν
with
EE = energy,hh = Plank's constant (6.62607 x 10-34 J s),νν= frequency
Since de Broglie believed particles and wave have the same traits, he hypothesized that the two energies would be equal:
mc2=hν(1.3)(1.3)mc2=hν
Because real particles do not travel at the speed of light, De Broglie submitted velocity (vv) for the speed of light (cc).
mv2=hν(1.4)(1.4)mv2=hν
Through the equation λλ, de Broglie substituted v/λv/λfor νν and arrived at the final expression that relates wavelength and particle with speed.
mv2=hvλ(1.5)(1.5)mv2=hvλ
Hence
λ=hvmv2=hmv(1.6)(1.6)λ=hvmv2=hmv
A majority of Wave-Particle Duality problems are simple plug and chug via Equation 1.61.6 with some variation of canceling out units
HOPE IT HELPS
#NKS23❤
@BEBRAINLY
MARK BRAINLIEST AND FOLLOW ME ALSO CLICK THANKS...
De Broglie Hypothesis...
In quantum mechanics, matter is believed to behave both like a particle and a wave at the sub-microscopic level. The particle behavior of matter is obvious. When you look at a table, you think of it like a solid, stationary piece of matter with a fixed location. At this macroscopic scale, this holds true. But when we zoom into the subatomic level, things begin to get more complicated, and matter doesn't always exhibit the particle behavior that we expect.
This non-particle behavior of matter was first proposed in 1923, by Louis de Broglie, a French physicist. In his PhD thesis, he proposed that particles also have wave-like properties. Although he did not have the ability to test this hypothesis at the time, he derived an equation to prove it using Einstein's famous mass-energy relation and the Planck equation.
Deriving the de Broglie Wavelength
De Broglie derived his equation using well established theories through the following series of substitutions:
De Broglie first used Einstein's famous equation relating matter and energy:
with
E = energy,m = mass,c = speed of light
Using Planck's theory which states every quantum of a wave has a discrete amount of energy given by Planck's equation:
E=hν(1.2)(1.2)E=hν
with
EE = energy,hh = Plank's constant (6.62607 x 10-34 J s),νν= frequency
Since de Broglie believed particles and wave have the same traits, he hypothesized that the two energies would be equal:
mc2=hν(1.3)(1.3)mc2=hν
Because real particles do not travel at the speed of light, De Broglie submitted velocity (vv) for the speed of light (cc).
mv2=hν(1.4)(1.4)mv2=hν
Through the equation λλ, de Broglie substituted v/λv/λfor νν and arrived at the final expression that relates wavelength and particle with speed.
mv2=hvλ(1.5)(1.5)mv2=hvλ
Hence
λ=hvmv2=hmv(1.6)(1.6)λ=hvmv2=hmv
A majority of Wave-Particle Duality problems are simple plug and chug via Equation 1.61.6 with some variation of canceling out units
HOPE IT HELPS
#NKS23❤
@BEBRAINLY
MARK BRAINLIEST AND FOLLOW ME ALSO CLICK THANKS...
Answered by
2
REFER TO THE GIVEN ATTACHMENT
☺☺☺
Attachments:
Similar questions