The decreasing order of nucleophilicities of the following is :
(I) `Br^(Ө)`
(II) `MeO^(Ө)`
(III) `Me_2 N^(Ө)`
(IV) `Me_3 C^(Ө)`.

Options

A. `(I) gt (II) gt (III) gt (IV)`
B. `(IV) gt (III) gt (II) gt (I)`
C. `(IV) gt (III) gt (I) gt (II)`
D. `(II) gt (I) gt (III) gt (IV)`

Explanation

To determine the decreasing order of nucleophilicities among the given species: (I) `Br^-`, (II) `MeO^-`, (III) `Me2N^-`, and (IV) `Me3C^-`, we can analyze their basicity and the factors that influence nucleophilicity.

### Step 1: Understand the concept of nucleophilicity
Nucleophilicity refers to the ability of a species to donate an electron pair to an electrophile. It is influenced by several factors, including charge, electronegativity, steric hindrance, and basicity.

### Step 2: Analyze the given nucleophiles
1. **`Br^-` (Bromide ion)**: This is a halide ion. Halides are generally good nucleophiles, but `Br^-` is relatively less nucleophilic compared to the other species listed here due to its larger size and lower basicity.

2. **`MeO^-` (Methoxide ion)**: This is a strong nucleophile due to the presence of a negative charge on oxygen, which is less electronegative than nitrogen. It is a stronger base than `Br^-`, hence a stronger nucleophile.

3. **`Me2N^-` (Dimethylamino ion)**: This species has a negative charge on nitrogen, which is a good nucleophile. It is more basic than `MeO^-`, making it a stronger nucleophile.

4. **`Me3C^-` (Tert-butyl anion)**: This is a highly sterically hindered nucleophile but is very basic. Despite the steric hindrance, it is still a strong nucleophile due to its high basicity.

### Step 3: Compare the nucleophilicity
- **`Me3C^-`** is the strongest nucleophile due to its high basicity.
- **`Me2N^-`** follows as it is also a strong nucleophile, but slightly less than `Me3C^-`.
- **`MeO^-`** is next, being a good nucleophile but less basic than the previous two.
- **`Br^-`** is the weakest nucleophile among the four due to its lower basicity and larger size.

### Final Order
Thus, the decreasing order of nucleophilicities is:
**(IV) `Me3C^-` > (III) `Me2N^-` > (II) `MeO^-` > (I) `Br^-`**