If the uncertainty in the position of a moving electron is equal to its de Broglie wavelength then its velocity will be completely uncertain. explain
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If the uncertainty in the position of a moving electron is equal to its de Broglie wavelength then its velocity will be completely uncertain. explain
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"If the uncertainty in the position of a moving electron is equal to its De Broglie Wavelength then it's velocity will be completely uncertain".This doesn't happen actually.
According to Heisenberg's Uncertainty Principle,
∆x.∆p > h/4π
or
∆x > h/4π ∆p
The De Broglie Wave equation,
w = h/mv
where w = wavelength.
It is given that ∆x is equal to w (which doesn't really happen ).
So , h/mv > h/4π∆p
We know, ∆p = m∆v
Cancelling h,
1/mv > 1/4πm∆v
∆v/v > 1/4π
Okay we got here that ∆v is directly proportional to v. So If v approaches infinity it would mean that ∆v will also approach infinity and hence become uncertain.
But practically speaking the value of 'v'> c(speed of light ).
Hope This Helps You!