If the position of an electron can be determined within $\pm 0.0001$ Å precision when momentum of electron is $\frac{h}{2 π a _{0}}$ , where $a_{0}$ is $0.529$ Å . Then find the ratio of minimum uncertainty in momentum to given momentum.
[h = 6.626 × 10^-34 ]

Question

If the position of an electron can be determined within $\pm 0.0001$ Å precision when momentum of electron is $\frac{h}{2 π a _{0}}$ , where $a_{0}$ is $0.529$ Å . Then find the ratio of minimum uncertainty in momentum to given momentum.

[h = 6.626 × 10^-34 ]

TestHub · Accepted Answer

Δ x = 0.0001 A ˚ Δ x × Δ p ⩾ 4 π h ​ ; Δ p = 4 π × 0.0001 A ˚ h ​ p = 2 π a 0 ​ h ​ a 0 ​ = 0.529 A ˚ p = 2 π × 0.529 A ˚ h ​ P Δ P ​ = 2 π × 0.529 A ˚ h ​ 4 π × 0.0001 A ˚ h ​ ​ = 4 π × 0.0001 A ˚ 2 π × 0.529 A ˚ ​ = 2 × 0.0001 0.529 ​ P Δ P ​ = 2 × 0.0001 0.529 ​ = 2645

Chemistry - Atomic Structure Question with Solution | TestHub

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