Prove that if uncertainty in position of a moving electron is equal to its de-Broglie wavelength than its velocity is completely uncertain?

Asked by fizajain21 | 18th Dec, 2020, 12:46: PM

Expert Answer:

According to heisenberg's uncertanity-
increment x equals lambda equals fraction numerator h over denominator m V end fraction
increment x cross times increment P greater-than or slanted equal to fraction numerator h over denominator 4 pi end fraction

increment P equals m increment V
fraction numerator h over denominator m V end fraction cross times m increment V greater-than or slanted equal to fraction numerator h over denominator 4 pi end fraction
fraction numerator increment V over denominator V end fraction greater-than or slanted equal to fraction numerator h over denominator 4 pi end fraction
V less or equal than 4 pi increment V
You can see Velcoity is uncertain.

Answered by Ravi | 22nd Dec, 2020, 07:27: PM