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Question

If the uncertainty in the position of an electron is zero, then the uncertainty in it's momentum would be _____.
  1. zero
  2. h/4π
  3. h/4π
  4. infinite


Solution

The correct option is D infinite
Heisenberg's uncertainty principle states that it is impossible to determine both the position and the momentum of an electron inside an atom simultaneously.

Mathematically, it is derived that the product of uncertainties in position and momentum is greater than or equal to a constant h4π. The equation for that is:

Δx.Δph4π where,

Δx = Uncertainty in position
Δp = Uncertainty in momentum 
 h = Planck's constant                             

Δph4π Δx

If the uncertainty in position, Δx = 0 then,
Δph4π .0
Δp =
(since, dividing any finite number by zero gives infinity)

therefore, uncertainty in momentum,  Δp = .

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