An electron, with a mass of 9.11×10−28 g is orbiting the nucleus of a hydrogen atom....

An electron, with a mass of 9.11×10−28 g is orbiting the nucleus of a hydrogen atom. A measurement determines the position of the electron to within ±1.63 nm. The velocity of the electron is measured as 6.39×106 m/s. What is the uncertainty in the velocity of the electron?

Solutions

Expert Solution

Given mass of electron, m = 9.11 * 10^-28 g = 9.11 * 10^-28 g * (1 kg / 1000g) = 9.11 * 10^-31 Kg

uncertainity in the position of electron, x = +/- 1.63 nm = +/- 1.63 * 10^-9 m

According to Heisenberg uncertainity principle,

x * P h / 4

=> x * (m * u) h / 4

=> (1.63 * 10^-9 m) * 9.11 * 10^-31 Kg * u ) (6.626 * 10^-34 m2Kg.s-1) / (4 * 3.14)

=> 1.485*10^-39 * u 5.2755*10^-35

=> u 3.55 * 10⁴ m/s

Hence uncertainity in the velocity of electron is 3.55 * 10⁴ m/s (answer)

queen_honey_blossom answered 1 year ago

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