Q- 2.61: If the position of the electron is measured within an accuracy of + 0.002 nm, calculate
the uncertainty in the momentum of the electron. Suppose the momentum of the
electron is h/4πm × 0.05 nm, is there any problem in defining this value.
Answer
From Heisenberg’s uncertainty principle,
Where,
Δx = uncertainty in position of the electron
Δp = uncertainty in momentum of the electron
Substituting the values in the expression of Δp:
= 2.637 × 10-23 Jsm-1
Δp = 2.637 × 10-23 kgms-1 (1 J = 1 kgms2s-1)
Uncertainty in the momentum of the electron = 2.637 × 10-23 kgms-1.
Actual momentum
= 1.055 × 10-24 kgms-1
Since the magnitude of the actual momentum is smaller than the uncertainty, the value cannot be defined.
Answer
From Heisenberg’s uncertainty principle,
Where,
Δx = uncertainty in position of the electron
Δp = uncertainty in momentum of the electron
Substituting the values in the expression of Δp:
= 2.637 × 10-23 Jsm-1
Δp = 2.637 × 10-23 kgms-1 (1 J = 1 kgms2s-1)
Uncertainty in the momentum of the electron = 2.637 × 10-23 kgms-1.
Actual momentum
= 1.055 × 10-24 kgms-1
Since the magnitude of the actual momentum is smaller than the uncertainty, the value cannot be defined.
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