Question

The speed of an electron is measured as 3.5 x 107 cm/sec with an
accuracy of 0.0098%. With what accuracy one can locate the
position of the electron?
​

Answer 1

Answer:

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

4πm

h

×0.05 nm,

Answer 2

Concept:

• According to Heisenberg's uncertainty principle, it is impossible to precisely measure or quantify an object's position or momentum.
• The wave-particle duality of matter serves as the foundation for this idea.

Given:

• Speed of electron v = 3.5 x 10^7 cm/s
• uncertainty in speed Δv = 0.0098% = 9.8 * 10^-5
• Planck's constant h =  6.626 * 10^-34
• Mass of an electron = 9.1 * 10^-31 kg

Find:

• The uncertainty of the position Δx

Solution:

We know from Heisenberg's uncertainty principle,

Δx Δp = h/4π

Δx  mΔv = h/4π

Δx = h/4πmΔv

Δx = 6.626 * 10^-34 /4π 9.1 * 10^-31  * 9.8 * 10^-5

Δx = 0.59

The uncertainty in the position of the electron is 0.59.

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