The probability of finding an electron at a point in space is proportional to the _____________ at that point.

• A. Absolute value of the wavefunction
• B. Square of its wavefunction
• C. Wave number
• D. Probability density

Answer: (B)

In quantum mechanics, the chance of finding an electron in a small region around a point is described by a probability density, which follows Born’s rule: the probability is proportional to the square of the wavefunction at that point. In other words, the probability density at a point is |ψ(r)|^2, and the probability of finding the electron in a small volume dV around that point is |ψ(r)|^2 dV. The magnitude of the wavefunction, |ψ|, by itself isn’t the probability because ψ can be negative or complex; squaring its magnitude makes the result a real, nonnegative density that can also exhibit interference via phase but still gives a meaningful probability when integrated over a region. The wave number is related to momentum, not to the probability density at a point. Remember, a point has zero probability in a strict sense; the useful quantity is the probability density, which is proportional to the square of the wavefunction.