Question

What is the uncertainty in the velocity of an electron whose position is known to within 2 x 10⁻⁸ meters? If the electron is moving at a speed of 5 x 10⁵ m/s, what fraction of this speed does the uncertainty represent?

Answer 1

The uncertainty in the velocity of an electron can be calculated using the Heisenberg uncertainty principle. The uncertainty in velocity is approximately 1.32 x 10^7 m/s and represents 2.64% of the electron's speed.

Step-by-step explanation:

The uncertainty in the velocity of an electron can be calculated using the Heisenberg uncertainty principle. According to the principle, the product of the uncertainties in position and momentum of a particle is always greater than or equal to Planck's constant divided by 4π. In this case, the position uncertainty is given as 2 x 10-8 meters. To find the velocity uncertainty, we need to divide Planck's constant by its mass. The resulting uncertainty in velocity is approximately 1.32 x 107 m/s.

To find the fraction of this uncertainty in velocity compared to the electron's speed of 5 x 105 m/s, we divide the uncertainty by the speed. This gives us the fraction as approximately 0.0264 or 2.64%