Question

An atom of argon has a radius of 71.pm and the average orbital speed of the electrons in it is about ×3.9107/ms. calculate the least possible uncertainty in a measurement of the speed of an electron in an atom of argon. write your answer as a percentage of the average speed, and round it to 2 significant digits.

Answer 1

Answer: 2.1 %

Explanation:

The radius of the Argon atom, r = 71 pm = 7.1 × 10 ⁻¹¹ m

Average orbital speed of electrons, v = 3.9 × 10⁷ m/s

From uncertainty principle:

Δx m Δv ≥ h/4π

mass of electron, m = 9.1 ×10⁻³¹ kg

Δx = radius of the argon atom = 7.1 × 10 ⁻¹¹ m

$\Rightarrow \Delta v = \frac {6.626 \times 10^{-34} m^2kg/s}{4\times 3.14 \times 7.1 \times 10^{-11} m \times 9.1 \times 10^{-31} kg}$

$\Delta v = 8.2 \times 10^5 m/s$

Percentage uncertainty:

$\frac{\Delta v}{v} \times 100\% = \frac {8.2 \times 10^5 m/s}{3.9 \times 10^7 m/s} \times 100 \%= 2.1 \%$