What is de-Broglie hypothesis? Obtain the relation for de-Broglie wavelength.
(July 2022)
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According to de Broglie, a moving material particle acts as a wave and sometimes wave is associated with moving material particle which controls the particle in every respect.
\(\lambda=\frac{h}{p}\)
where p = Momentum of the particle
h = Planck constant
De-Broglie equated the energy equation of Plank (wave nature) and Einstein (particle nature) such that,
$E = hv$ (Plank energy relation)
$E = mc^2$ (Einsteins mass-energy relation)
Where,
E = energy associated with the particle
h = planks constant
v = frequency associated with the particle
m = moss of the particle
c = speed of light
After equating equations (1) and (2) we get:
$hv = mc^2$
\(h \frac{ c }{\lambda}= mc ^2 \quad \ldots\left(\because v =\frac{ c }{\lambda}\right)\)
\(\lambda=\frac{ hc }{ mc ^2}=\frac{ h }{ mc }\)
If the particle is moving with velocity 'v' then equation (3) becomes,
\(\lambda=\frac{ h }{ mv }\)
\(\lambda=\frac{h}{p}\)
where p = Momentum of the particle
h = Planck constant
De-Broglie equated the energy equation of Plank (wave nature) and Einstein (particle nature) such that,
$E = hv$ (Plank energy relation)
$E = mc^2$ (Einsteins mass-energy relation)
Where,
E = energy associated with the particle
h = planks constant
v = frequency associated with the particle
m = moss of the particle
c = speed of light
After equating equations (1) and (2) we get:
$hv = mc^2$
\(h \frac{ c }{\lambda}= mc ^2 \quad \ldots\left(\because v =\frac{ c }{\lambda}\right)\)
\(\lambda=\frac{ hc }{ mc ^2}=\frac{ h }{ mc }\)
If the particle is moving with velocity 'v' then equation (3) becomes,
\(\lambda=\frac{ h }{ mv }\)
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