A nonrelativistic electron has a kinetic energy of 5.4 eV.What is the energy of a photon whose wavelength is the same as the de Broglie wavelength of the electron? ,c = 3.00 × 10⁸ m/s,1 eV = 1.60 × 10^-19 J) A) 2.4 keV B) 2.2 keV C) 2.0 keV D) 2.5 keV E) 2.7 keV

Question

Quizplus · Accepted Answer

The de Broglie wavelength of the electron is given by:

λ = h/(mv)

where h is Planck's constant, m is the mass of the electron, and v is the velocity of the electron.

The velocity of the electron can be determined using its kinetic energy:

K.E. = (1/2)mv^2
v = √(2K.E./m)

Substituting this expression for v into the expression for the de Broglie wavelength, we get:

λ = h/√(2K.E.m)

The energy of a photon is given by:

E = hc/λ

where c is the speed of light.

Substituting the expression for λ we just derived, we get:

E = hc/ (h/√(2K.E.m))
E = √(2K.E.m)c

Substituting the given values for the kinetic energy of the electron, m and c, we get:

E = √(2 × 5.4 × 1.60 × 10^-19 × 9.11 × 10^-31 × 3.00 × 10^8)
E ≈ 2.4 keV

Therefore, the answer is A) 2.4 keV.

A Nonrelativistic Electron Has a Kinetic Energy of 5