An electron is placed in a box about the size of an atom that is about 1 ｘ 10⁻¹⁰ m. What is the velocity of the electron?  (Answer: 7.29 ｘ 10⁶ m s⁻¹)



Given:

Size of the box = Δx = 1 ｘ10⁻¹⁰ m 

∴ Plank's Constant = h =  6.626 ｘ 10⁻³⁴ m² kg s⁻¹
∴ Mass of the electron = m = 9.11 ｘ 10⁻³¹ kg

To Find:

The velocity of an electron = Δv = ?



Solution:

According to Heisenberg's uncertainty principle, 

Δx ΔP ≈ h

Where (ΔP = m Δv) So,

Δx m Δv ≈ h

or

Δv ≈ `\frac {h}{Δx m}` --------------(1)

Now putting the corresponding values in equation (1)

Δv ≈ `\frac {6.626 ｘ 10⁻³⁴ m² kg s⁻¹}{9.1 ｘ 10⁻³¹ kg ｘ 1 ｘ10⁻¹⁰ m }`

Δv ≈ `\frac {6.626 ｘ 10⁻³⁴ kg m² s⁻¹}{9.1 ｘ 10⁻⁴¹ kg m }`

Δv ≈ 0.728 ｘ 10⁻⁷ m s⁻¹

Δv ≈ 7.28 ｘ 10⁻⁶ m s⁻¹--------------------Ans.



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