For the cell`:`
`TI|TI^(o+)(10^(-3)M)||Cu^(2+)(10^(-1)M)|Cu`
`E_(cell)` can be increased by
`a. ` Decreasing `[Cu^(2+)]." "b.` Decreasing `[TI^(o+)]`
`c.` Increasing `[Cu^(2+)] " "d. Increasing by `[TI^(o+)]`

Explanation

To solve the problem, we need to analyze the electrochemical cell given by the notation:

**Cell Notation: TI | TI^(o+) (10^(-3) M) || Cu^(2+) (10^(-1) M) | Cu**

### Step 1: Identify the half-reactions
In the given cell, we have two half-reactions:
1. At the anode (oxidation):
\[ \text{TI} \rightarrow \text{TI}^{+} + e^{-} \]
2. At the cathode (reduction):
\[ \text{Cu}^{2+} + 2e^{-} \rightarrow \text{Cu} \]

### Step 2: Balance the half-reactions
To balance the number of electrons transferred, we multiply the anode reaction by 2:
\[ 2 \text{TI} \rightarrow 2 \text{TI}^{+} + 2e^{-} \]
Now, the overall balanced reaction is:
\[ 2 \text{TI} + \text{Cu}^{2+} \rightarrow 2 \text{TI}^{+} + \text{Cu} \]

### Step 3: Write the Nernst equation
The Nernst equation for the cell can be expressed as:
\[ E_{\text{cell}} = E^{\circ}_{\text{cell}} - \frac{0.0591}{n} \log Q \]
Where:
- \(E^{\circ}_{\text{cell}}\) is the standard cell potential.
- \(n\) is the number of moles of electrons transferred (which is 2).
- \(Q\) is the reaction quotient.

### Step 4: Determine the reaction quotient \(Q\)
For the reaction:
\[ Q = \frac{[\text{TI}^{+}]^2}{[\text{Cu}^{2+}]} \]
Given the concentrations:
- \([\text{TI}^{+}] = 10^{-3} \, M\)
- \([\text{Cu}^{2+}] = 10^{-1} \, M\)

Substituting these values into \(Q\):
\[ Q = \frac{(10^{-3})^2}{(10^{-1})} = \frac{10^{-6}}{10^{-1}} = 10^{-5} \]

### Step 5: Analyze how to increase \(E_{\text{cell}}\)
To increase \(E_{\text{cell}}\), we need to decrease the value of \(Q\) in the logarithmic term of the Nernst equation. This can be achieved by:
- **Decreasing \([\text{Cu}^{2+}]\)**: This will decrease the denominator in \(Q\), thus increasing \(E_{\text{cell}}\).
- **Increasing \([\text{TI}^{+}]\)**: This will increase the numerator in \(Q\), thus decreasing \(Q\) and increasing \(E_{\text{cell}}\).

### Step 6: Evaluate the options
Given the options:
- a. Decreasing \([\text{Cu}^{2+}]\) → Increases \(E_{\text{cell}}\)
- b. Decreasing \([\text{TI}^{+}]\) → Decreases \(E_{\text{cell}}\)
- c. Increasing \([\text{Cu}^{2+}]\) → Decreases \(E_{\text{cell}}\)
- d. Increasing \([\text{TI}^{+}]\) → Increases \(E_{\text{cell}}\)

### Conclusion
The correct options that can increase \(E_{\text{cell}}\) are:
- **a. Decreasing \([\text{Cu}^{2+}]\)**
- **d. Increasing \([\text{TI}^{+}]\)**

### Final Answer
The options that can increase \(E_{\text{cell}}\) are **a** and **d**.

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