The correct answer is option 'D' - (2n - 1)/3. Let's break down the reasoning behind this answer:

1. Understanding the problem:
- We are given a rooted tree with n nodes.
- Each node in the tree can have either 0 or 3 children.
- We need to determine the number of leaf nodes in this tree.

2. Observations:
- In a rooted tree, a leaf node is a node that has no children.
- Each node in the tree can have either 0 or 3 children.
- The tree can be visualized as a binary tree where each node has either 0 or 2 children.
- The total number of nodes in the binary tree representation of the given tree is (2n - 1).

3. Conversion to a binary tree:
- We can convert the given tree into a binary tree representation by replacing each node with 0 children with a node that has 2 children (null nodes).
- This conversion does not change the number of leaf nodes in the tree.

4. Relationship between nodes and leaf nodes:
- In a binary tree, the number of leaf nodes (L) can be calculated using the formula L = (N + 1)/2, where N is the total number of nodes.
- In the given tree, the total number of nodes is (2n - 1) after the conversion to a binary tree.
- Substituting N = (2n - 1) in the formula, we get L = ((2n - 1) + 1)/2 = (2n - 1)/2.

5. Accounting for the fact that each node can have either 0 or 3 children:
- In the original tree, each node can have either 0 or 3 children, which means that there are extra nodes in the binary tree representation.
- For every node with 3 children, we have 2 extra nodes in the binary tree representation.
- So, the total number of extra nodes is 2 * (number of nodes with 3 children).
- The number of nodes with 3 children can be calculated as (n - L), where n is the total number of nodes and L is the number of leaf nodes.
- Therefore, the total number of nodes in the binary tree representation is (2n - 1) + 2 * (n - L).

6. Final calculation:
- Substituting L = (2n - 1)/2 and simplifying the expression, we get (2n - 1) + 2 * (n - (2n - 1)/2).
- Simplifying further, we get (2n - 1) + 2n - (2n - 1) = 4n - 2.
- The number of leaf nodes in the tree is equal to the number of nodes in the binary tree representation, which is (4n - 2).
- Dividing by 3 to account for the fact that each node can have either 0 or 3 children, we get (4n - 2)/3, which is equivalent to (2n - 1)/3.

Therefore, the correct answer is option 'D' - (2n - 1)/3.