Question

The Radial wave function for 2p orbital is:

• A. $2(\frac{z}{a_{0}})^{\frac{3}{2}}e^{-\sigma}$
• B. $2^{-\frac{3}{2}}(\frac{z}{a_{0}})^{\frac{3}{2}}(e^{-\sigma})e^{-\frac{\sigma}{2}}$
• C. $2^{-1}(\frac{z}{a_{0}})^{\frac{3}{2}}\sigma e^{-\frac{\sigma}{2}}$
• D. $2^{-1}(\frac{z}{a_{0}})^{\frac{3}{2}}(1-\sigma)e^{-\frac{\sigma}{2}}$

Hint:

2p has 0 radial nodes, so look for the simplest version with a '$\sigma$' term but no subtraction factor like $(1-\sigma)$.

Answer 1

The Correct Option is C

Step 1: Concept Radial wave functions ($R_{n,l}$) describe the probability of finding an electron at a distance $r$ from the nucleus.

Step 2: Meaning The form of the function depends on the principal quantum number ($n$) and azimuthal quantum number ($l$).

Step 3: Analysis For a 2p orbital ($n=2, l=1$), the radial part contains a term proportional to $\sigma$ (where $\sigma$ is related to $r$) and an exponential decay term $e^{-\sigma/2}$. It does not have any radial nodes (since $n-l-1 = 0$), so there is no $(1-\sigma)$ factor.

Step 4: Conclusion Option (C) correctly identifies the mathematical form for the 2p radial wave function. Final Answer: (C)