Question

(a) How much time is needed to measure the kinetic energy of an electron whose speed is 100 m s^-1 with an uncertainty of no more than 0.1 percent? How far will the electron have travelled in this period of time? (b) Make the same calculations for a 1 g insect whose speed is the same. What do these sets of figures indicate?

Answer 1

Kinetic energy of the electron is:

E = (1/2)mv² = 4.55 x 10^-27 J

and uncertainty should not be more than 0.1%

so,

using the Uncertainty Principle relation between Energy and time, the time that is needed to measure the Kinetic energy will be:

in this time, the distance which it would have traveled will be:

x = 100 x 1.158 x 10^-5 = 1.158 x 10^-3 m = 1.158 mm.

b]

For an insect with mass m = 1 g = 1 x 10^-3 kg

the uncertainty in kinetic energy will be:

therefore, time needed to measure its kinetic energy will be:

These figures indicate that the macroscopic insect has such a large kinetic energy owing to its large mass, that the time in which its kinetic energy can be determined is almost zero and the process of measuring is nearly instantaneous.