Step 1: Understand water potential.
Water potential is represented by the symbol:
\[
\Psi_w
\]
It determines the direction of water movement.
Water always moves from a region of higher water potential to a region of lower water potential.
In other words, water moves from less negative water potential to more negative water potential.
Step 2: Understand the path of water movement in roots.
In roots, water enters through root hairs.
Then it moves through cortical cells.
Finally, it reaches the xylem vessels.
So, the path of water movement is:
\[
\text{Root hairs} \rightarrow \text{Cortex} \rightarrow \text{Xylem}
\]
Step 3: Apply the water potential rule.
For water to move from root hairs to cortex and then to xylem, the water potential must gradually decrease along this path.
That means:
\[
\Psi_w \text{ of root hairs} > \Psi_w \text{ of cortex} > \Psi_w \text{ of xylem}
\]
Since \(0\) is greater than \(-1\), and \(-1\) is greater than \(-2\), the correct gradient is:
\[
0 > -1 > -2
\]
Step 4: Check option (1).
Option (1) gives:
\[
\text{Root hairs}=0
\]
\[
\text{Cortex}=-1
\]
\[
\text{Xylem}=-2
\]
This follows the correct decreasing water potential gradient:
\[
0 \rightarrow -1 \rightarrow -2
\]
Therefore, water can move from root hairs to cortex and then to xylem.
Step 5: Reject the other options.
In option (2), cortex has \(-2\) and xylem has \(-1\).
Water would not naturally move from cortex \((-2)\) to xylem \((-1)\), because \(-1\) is higher water potential than \(-2\).
In option (3), xylem has \(0\), which is higher than both root hairs and cortex.
So water would not move toward xylem.
In option (4), root hairs have the lowest water potential \((-2)\), so water would not move away from root hairs toward cortex and xylem.
Step 6: Final conclusion.
Hence, water movement from root hairs to xylem through cortex occurs when the water potentials are:
\[
\text{Root hairs}=0,\quad \text{Cortex}=-1,\quad \text{Xylem}=-2
\]
Therefore,
\[
\boxed{\text{Root hairs }=0,\ \text{Cortex }=-1,\ \text{Xylem }=-2}
\]