Question

If the radial wavefunction of the 3p orbital of a hydrogen-like atom is

Hint:

Radial nodes are obtained by setting radial part equal to zeroIgnore exponential terms and solve polynomial part

Answer 1

Correct Answer: 6

Step 1: Node condition.
A radial node is where the wavefunction is zero, which from the given form needs $4 - \rho = 0$, so $\rho = 4$.

Step 2: Substitute $\rho$ for $n = 3$.
\[ 4 = \frac{2Z}{3a_0} r \]

Step 3: Solve for r.
\[ r = \frac{6a_0}{Z} \Rightarrow Y = 6 \]

Step 4: Answer.
\[ \boxed{6} \]