The ionisation potential for the atoms of a gas is $I$ - AQA - A-Level Physics - Question 17 - 2019 - Paper 2

To derive the speed $v$, we start from the relationship between kinetic energy and ionisation potential. The kinetic energy (KE) of an electron can be expressed as:

$KE = \frac{1}{2}mv^2$

The ionisation potential $I$ represents the energy required to ionise an atom. For the electron to just cause ionisation, its kinetic energy must equal the ionisation potential:

$\frac{1}{2}mv^2 = I$

Rearranging this equation to solve for $v$ gives:

$v^2 = \frac{2I}{m}$

Taking the square root of both sides results in:

$v = \sqrt{\frac{2I}{m}}$

Thus, the answer corresponds to option A from the multiple-choice answers.