Question

uncertainty in position of an electron is 1 nm calculate the uncertainty in velocity. ​

Answer 1

Answer:

Answer: We have the relation, (∆ x) /(∆ v) = h/4πm......... 1Here, h= 6.626x 10^-34 JS= 6.626x 10^-27 erg sec, ∆ x= 1 nm= 1x 10^-7 cmWe know, m= 9.1x 10^-28 g∆ v= 6.626x 10^-27 erg sec/4x 3.142x 9.1x 10^-28 gx 1x 10^-7 CM= 6.62x 10^-27 /114.37x 10^-35 CM/sec= 0.579x 10^ 7 CM/ sec.... Thank you

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Answer 2

the uncertainty in velocity is  5.79 × 10⁴ ms⁻¹ (approximately)

- given : uncertainty in position, Δx = 1 nm

                                                          = 10⁻⁹ m

- we know that: h = 6.626 × 10⁻³⁴

                         m = 9.1  × 10⁻³¹

- By heisenberg's uncertainty principle, we know that

   Δx × Δv = h/4πm

- putting all these values in the formula, we get

   10⁻⁹ × Δv = (6.626 × 10⁻³⁴) / (4 × 3.14 × 9.1  × 10⁻³¹)

              Δv = (0.0579 × 10⁻³) / 10⁻⁹

              Δv = 0.0579 × 10⁶ ms⁻¹

              Δv = 5.79 × 10⁴ ms⁻¹