Question

the electron in the ground-state of hydrogen has an uncertainty in its position on the order of 10-10 m. use heisenberg's uncertainty principle to estimate the average speed of the electron (hint: in the ground state, the electron's speed should be roughly equal to the uncertainty in its velocity). what fraction of the speed of light is this value?

Answer 1

The average speed of the electron in the ground-state of hydrogen is estimated to be 10^-10 m/s. This is a very small fraction of the speed of light.

Step-by-step explanation:

The Heisenberg uncertainty principle states that it is impossible to simultaneously know the exact position and velocity of a subatomic particle. In the ground-state of hydrogen, the uncertainty in the electron's position is approximately 10^-10 m. Since the electron's speed in the ground state is roughly equal to the uncertainty in its velocity, we can estimate the average speed to be approximately 10^-10 m/s.

To determine the fraction of the speed of light, we can use the equation:

fraction of the speed of light = (average speed of electron) / (speed of light)

Substituting the values, we get:

fraction of the speed of light = (10^-10 m/s) / (3 x 10^8 m/s)

which simplifies to:

fraction of the speed of light ≈ 3.33 x 10^-19