Question : If the uncertainty in position and momentum are equal, the uncertainty in velocity will be:
Option 1: √h/π
Option 2: 1/2m√h/π
Option 3: √h/2π
Option 4: √h/2πm
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Correct Answer: 1/2m√h/π
Solution : The correct option is 1/2 m√h/π .
According to Heisenberg's uncertainty principle, ∆x.∆p = h/π; ∆x.m∆v = h/4π. Given ∆x = m∆v; m∆v.m∆v = h/4π; m 2 ∆v 2 = h/4π; ∆v = √ h/4π × 1/m; ∆v = 1/2 m × √h/π
According to Heisenberg's Uncertainty Principle, if the uncertainty in position and momentum is equal, it implies that there is a fundamental limit to the precision with which both values can be known simultaneously. The uncertainty in velocity will also be equal, as velocity is directly related to momentum.
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