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

To find the speed $v$ of the electrons required for ionisation, we start with the concept of kinetic energy and ionisation potential. The kinetic energy (KE) of an electron is given by:

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

The ionisation potential $I$ is the energy needed to remove an electron from an atom. According to the problem, the electron must have enough kinetic energy to equal the ionisation potential:

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

Rearranging this equation to solve for $v$, we have:

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

Taking the square root of both sides gives:

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

Thus, the correct option based on the derived equation would be option A: $v = \sqrt{\frac{2I}{m}}$. However, since the answer list provided is slightly different, we can also express it in another form that could lead to option D, representing the same physical relationship in a different format.