To solve the question regarding the radial probability curves and determine which statements are correct, we will analyze each statement step by step.
### Step 1: Understand the 2s Orbital
- The 2s orbital has a principal quantum number (n) of 2.
- The formula for the total number of nodes in an orbital is \( n - 1 \).
- For the 2s orbital, the total number of nodes is \( 2 - 1 = 1 \).
**Hint:** Remember that the total number of nodes is derived from the principal quantum number.
### Step 2: Analyze the Number of Maxima in the 2s Orbital
- The radial probability curve for the 2s orbital shows that there are two maxima.
- This means that there are two positions where the probability of finding an electron is highest.
**Hint:** Visualizing the radial probability curve can help in understanding the maxima.
### Step 3: Check the Formula for Radial Nodes
- The formula for the number of radial nodes is \( n - l - 1 \), where \( l \) is the azimuthal quantum number.
- For the 2s orbital, \( l = 0 \) (since s orbitals have \( l = 0 \)).
- Thus, the number of radial nodes is \( 2 - 0 - 1 = 1 \).
**Hint:** The azimuthal quantum number \( l \) varies with the type of orbital (s, p, d, f).
### Step 4: Evaluate Angular Nodes
- The number of angular nodes is equal to \( l \).
- For the s orbital, \( l = 0 \), so there are 0 angular nodes.
- For p orbitals, \( l = 1 \) (1 angular node), and for d orbitals, \( l = 2 \) (2 angular nodes).
**Hint:** The number of angular nodes is directly related to the type of orbital.
### Step 5: Analyze the Statement about 3d2
- The statement claims that the 3d2 orbital has 3 angular nodes.
- For d orbitals, \( l = 2 \), which means there are 2 angular nodes, not 3.
- Therefore, this statement is incorrect.
**Hint:** Remember that the number of angular nodes is equal to the azimuthal quantum number \( l \).
### Conclusion
Based on the analysis:
- The first statement about the 2s orbital having 2 maxima is **true**.
- The second statement regarding the formula for radial nodes \( n - l - 1 \) is **true**.
- The third statement about the number of angular nodes being \( l \) is **true**.
- The last statement about 3d2 having 3 angular nodes is **false**.
Thus, the correct statements are A, B, and C.
### Final Answer
The correct statements regarding the radial probability curves are:
- A: The number of maxima in a 2s orbital are 2.
- B: The number of spherical or radial nodes is equal to \( n - l - 1 \).
- C: The number of angular nodes are \( l \).
**Incorrect Statement:**
- D: 3d2 has 3 angular nodes (this is false; it has 2 angular nodes).
