Question

Which statement A-D about the wave function for a single electron is not correct?

A. A French graduate student named Louis de Broglie first had the idea that an electron should
B. Since νλ = c, an expression for the wavelength of an electron can be found by combining Einstein's equation that relates mass and energy (E = mc2) with his equation that gives the energy of a photon in terms of its frequency (E = hν).
C. The square of the wave function's amplitude at a particular point in space gives the probability density of finding an electron at that point.
D. Wave functions can have nodes, which are points where the amplitude is zero.
E. Statements A-D are all correct.

Answer 1

The incorrect statement about the wave function is B, which inaccurately suggests that the equation νλ = c can be used for electrons when in fact, electrons use λ = h/p as per de Broglie's hypothesis.

Step-by-step explanation:

The statement about the wave function for a single electron that is not correct is B. This statement claims, "Since νλ = c, an expression for the wavelength of an electron can be found by combining Einstein's equation that relates mass and energy (E = mc2) with his equation that gives the energy of a photon in terms of its frequency (E = hν)." This is incorrect because the equation νλ = c is specific to electromagnetic waves traveling at the speed of light, and it cannot be directly applied to electrons which do not travel at the speed of light. Louis de Broglie's hypothesis for the wave nature of particles such as electrons uses a different equation, λ = h/p, where λ is the wavelength, h is Planck's constant, and p is the momentum of the electron.

The correct concepts related to electrons wave functions include:

• Louis de Broglie's proposition that an electron can be described as a wave.
• The interpretation that the square of the wave function's amplitude gives the probability density of finding an electron at a particular point in space.
• The fact that wave functions can have nodes, which are points where the amplitude is zero, representing points where the probability of finding the electron is zero.