Heisenberg's <em>Uncertainty Principle</em> gives a relationship between the standard deviation of an object's position and its momentum.
where
- the standard deviation of the object's <em>momentum,</em>
- the standard deviation of the object's <em>position, </em>and
- the Planck's constant.
By definition, the momentum of the electron equals the product of its mass and velocity.
Assuming that measurement of the mass of the electron is accurate. It is assumed to be a coefficient of constant value. The <em>standard deviation</em> in the electron's velocity is thus directly related to that of its mass. That is:
from the question;
Convert the unit of the Planck's constant to base SI units (kg, m, s, etc.) if it was provided in derived units such as joules. Doing so would allow for a dimension analysis on the accuracy of the result.
Apply the <em>Uncertainty Principle</em>:
.
Dimensional analysis:
resembles the <em>standard deviation</em> of a position measurement. It is expected to have a unit of meter, which is the same as that of position.