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The wave function for the 2s orbital of hydrogen is given by: psi = (1/(4*sqrt(2))) * (1/a0)^(3/2) * (2 - r/a0) * e^(-r/(2*a0)), where a0 = 0.529 Angstrom is the first Bohr radius. Identify the correct statement(s).

1. The number of radial nodes is equal to three
2. The probability density is independent of direction
3. The number of radial nodes is equal to 1
4. The radial node occurs at a distance 2*a0 from the nucleus

Correct answer: The probability density is independent of direction

Solution

For 2s: n=2, l=0. Number of radial nodes = n-l-1 = 1 (option C correct; option A wrong). The wave function psi depends only on r (no theta or phi), so psi² is spherically symmetric — independent of direction (option B correct). Radial node: set 2-r/a0=0 -> r=2*a0 (option D correct). Options B, C, and D are all correct statements; A is incorrect.

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