What is the
(a) momentum,
(b) speed, and
(c) de Broglie wavelength of an electron with kinetic energy of 120 eV.
Kinetic energy of the electron, Ek = 120 eV
Planck’s constant, h = 6.6 × 10−34 Js
Mass of an electron, m = 9.1 × 10−31 kg
Charge on an electron, e = 1.6 × 10−19 C
(a) For the electron, we can write the relation for kinetic energy as: Ek = 1/2 mv2
Where, v = Speed of the electron
Momentum of the electron, p = mv = 9.1 × 10−31 × 6.496 × 106 = 5.91 × 10−24 kg ms−1
Therefore, the momentum of the electron is 5.91 × 10−24 kg m s−1 .
(b) Speed of the electron, v = 6.496 × 106 m/s
(c) De Broglie wavelength of an electron having a momentum p, is given as: λ = h/p = 6.6 x 10-34 / 5.91 x 10-24 = 1.116 x 10-10 m = 0.112 nm
Therefore, the de Broglie wavelength of the electron is 0.112 nm.
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