Physics Asked on May 18, 2021
De-broglie equation for uncharged particle:
$$lambda= frac{h}{sqrt{2mE}}$$
Where,
$lambda$ = wavelength
$h$ = planks constant
$m$ = mass of uncharged particles
The de Broglie wavelength is the wavelength, $λ$, associated with a massive particle (i.e., a particle with mass, as opposed to a massless particle) and is related to its momentum, $p$, through the Planck constant, $h$:
$$lambda= frac{h}{p}$$
For non-relativistic particle, Total energy of free particle $$E=frac{p^2}{2m}Rightarrow p=sqrt{2mE}$$ $$lambda= frac{h}{sqrt{2mE}}$$
In relativistic-case, Using two formulas from special relativity, one for the relativistic mass-energy and one for the relativistic momentum
$$p=gamma m_0 v$$ $$Rightarrow lambda=frac{h}{gamma m_0 v}$$
Answered by Young Kindaichi on May 18, 2021
$E$ here is the kinetic energy, not the total energy.
The original formula is $lambda=h/p$, and then $p$ is obtained from the (non-relativistic) formula $E={1over 2} m v^2 = p^2/2m$
Answered by RogerJBarlow on May 18, 2021
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