For a free electron with 100 keV kinetic energy, calculate the: a) electron speed b) electron...

Question

Question

For a free electron with 100 keV kinetic energy, calculate the:

a) electron speed

b) electron momentum

c) de Broglie wavelength of the electron

Answer 1

Answer #1

a) Energy in J = Energy in eV * 1.6 * 10^-19 = 100 * 10³ * 1.6 * 10^-19 = 1.6 * 10^-14 J

We have the relation : E = 1/2 * m * v², where m is mass and v is velocity

We use the above energy and value of m to solve for v:

1.6 * 10^-14 = 1/2 * 9.11 * 10^-31 * v²

Solving, we get: v = 7.02 * 10⁸ m/s

b) momentum = m * v = 9.11 * 10^-31 * 7.02 * 10⁸ = 6.40 * 10^-22 kg m/s

c) De broglie waverlength = h / momentum, where h is planck's constant

= 6.625 * 10^-34 / (6.40 * 10^-²² ) = 1.04 * 10^-12 m

Answer 2

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