Question

Uncertainty in the position of an electron (mass 9.1×10^-31) moving with a velocity 600m/s, accurate
upto 0.001% will be
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Answer 1

Given :-

◉ Electron which has a mass of 9.1 × 10⁻³¹ moving with a velocity 600 m/s

To Find :-

◉ Uncertainty in position accurate upto 0.001%

Solution :-

Uncertainty in the position or momentum of an electron is given by,

⇒ ∆x.m∆v = h/4π

It is given that the uncertainty in the velcity 0.001% of the original velocity i.e., 600 m/s

So,

⇒ ∆v = 600 × 0.001 / 100

⇒ ∆v = 6 × 10⁻³ m/s

Putting values in the equation, we have

⇒ ∆x × 9.1 × 10⁻³¹ × 6 × 10⁻³ = 6.6 × 10⁻³⁴ / 4π

⇒ ∆x × 54.6 × 10⁻³ = 1.65 / π

⇒ ∆x × 54.6 = 0.5225 [ π = 3.14 ]

⇒ ∆x × 54.6 = 0.5225

⇒ ∆x × 54.6 = 52.25 × 10⁻²

⇒ ∆x = 0.95 × 10⁻²

⇒ ∆x = 9.5 × 10⁻³ m

Hence, Uncertainty in the position will be 9.5 × 10⁻³ m

Some Information :-

☛ The Heisenberg uncertainty principle states that we cannot find the momentum and position simultaneously with accuracy. If you measure momentum accurately there were would be more uncertainty in position and vice-versa.

∆x . m∆v ≥ h / 4π