Quantum Mechanics - Wave Function

Which of the following functions could represent the radial wave function for an electron in an atom? (r is the distance of the electron from the nucleus; A and b are constants.)
I. Ae^−br
II. A sin (br)
III. A/r

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III

(GR0177 #30)

Solution:

Property of a wave function: Ψ is finite.
Ψ(r → ∞) and Ψ(r → 0) cannot be ∞.

Ψ(r → ∞) = Ae^−∞ → 0 
Ψ(r → 0) = Ae⁻⁰ → A
I. TRUE

Ψ(r → ∞) = A sin ∞ ↛ 0.
II. FALSE

Ψ(r → 0) = A/0 → ∞.
III. FALSE

Answer: A