In an electron microscope, electrons are accelerated to great velocities. Calculate the wavelength of an electron traveling with a velocity of 7.0 * 10³ kilometers per second. The mass of an electron is 9.1 * 10^-28 g. A)1.0 * 10^-13 m B)1.0 * 10^-7 m C)1.0 m D)1.0 * 10^-10 m

Question

Quizplus · Accepted Answer

The wavelength of an electron is given by:

λ = h / p

where h is Planck's constant and p is the momentum of the electron. Since the electron is traveling at high velocities, we cannot use its mass to calculate the momentum. Instead, we use the relativistic equation:

p = mv / sqrt(1 - (v/c)^2)

where m is the mass of the electron, v is its velocity, and c is the speed of light.

Substituting the values given in the problem, we get:

p = (9.1 x 10^-28 kg) * (7.0 x 10^13 m/s) / sqrt(1 - (7.0 x 10^13 m/s / 3.0 x 10^8 m/s)^2)

p = 1.23 x 10^-18 kg m/s

Now we can calculate the wavelength:

λ = h / p = 6.63 x 10^-34 J s / 1.23 x 10^-18 kg m/s = 5.4 x 10^-10 m

This is equivalent to 0.54 nanometers or 1.0 x 10^-10 meters, which is answer D.

In an Electron Microscope, Electrons Are Accelerated to Great Velocities