How many of the following obey's Sidgwick EAN rule ?
`(a) K_(4)[Fe(CN)_(6)]," "(b) K_(3)[Fe(CN)_(6)]`,
`(c ) Mn_(2)(CO)_(10)," "(d) [Fe(H_(2)O)_(5)NO]SO_(4)`,
`(e ) Na_(2)[Fe(CN)_(5)NO]," "(f) [Co_(2)(CO)_(8)]`,
`(g) [Fe(pi-C_(5)H_(5))_(2)]`

Explanation

To determine how many of the given coordination compounds obey Sidgwick's Effective Atomic Number (EAN) rule, we will analyze each compound step by step. The EAN rule states that the effective atomic number of the central metal atom in a coordination complex should equal the atomic number of the nearest noble gas.

### Step-by-Step Solution:

1. **Identify the Coordination Compounds:**
- (a) K₄[Fe(CN)₆]
- (b) K₃[Fe(CN)₆]
- (c) Mn₂(CO)₁₀
- (d) [Fe(H₂O)₅NO]SO₄
- (e) Na₂[Fe(CN)₅NO]
- (f) [Co₂(CO)₈]
- (g) [Fe(π-C₅H₅)₂]

2. **Calculate EAN for each compound:**
- **(a) K₄[Fe(CN)₆]:**
- Atomic number of Fe = 26
- CN donates 2 electrons, total from 6 CN = 6 × 2 = 12
- Oxidation state of Fe = +2 (since K₄[Fe(CN)₆] has a charge of -4)
- EAN = 26 + 12 - 2 = 36 (Noble gas configuration)
- **Obeys EAN rule.**

- **(b) K₃[Fe(CN)₆]:**
- Atomic number of Fe = 26
- Oxidation state of Fe = +3
- EAN = 26 + 12 - 3 = 35 (Does not match noble gas configuration)
- **Does not obey EAN rule.**

- **(c) Mn₂(CO)₁₀:**
- Atomic number of Mn = 25
- CO donates 2 electrons, total from 10 CO = 10 × 2 = 20
- Oxidation state of Mn = 0 (neutral complex)
- EAN = (25 + 20) × 2 = 90 (per metal atom = 45, does not match noble gas configuration)
- **Does not obey EAN rule.**

- **(d) [Fe(H₂O)₅NO]SO₄:**
- Atomic number of Fe = 26
- H₂O donates 2 electrons, total from 5 H₂O = 5 × 2 = 10
- NO donates 3 electrons.
- Oxidation state of Fe = +2 (due to SO₄²⁻)
- EAN = 26 + 10 + 3 - 2 = 37 (Does not match noble gas configuration)
- **Does not obey EAN rule.**

- **(e) Na₂[Fe(CN)₅NO]:**
- Atomic number of Fe = 26
- CN donates 2 electrons, total from 5 CN = 5 × 2 = 10
- NO donates 3 electrons.
- Oxidation state of Fe = +3
- EAN = 26 + 10 + 3 - 3 = 36 (Noble gas configuration)
- **Obeys EAN rule.**

- **(f) [Co₂(CO)₈]:**
- Atomic number of Co = 27
- CO donates 2 electrons, total from 8 CO = 8 × 2 = 16
- Oxidation state of Co = 0 (neutral complex)
- EAN = (27 + 16) × 2 = 86 (per metal atom = 43, does not match noble gas configuration)
- **Does not obey EAN rule.**

- **(g) [Fe(π-C₅H₅)₂]:**
- Atomic number of Fe = 26
- π-C₅H₅ donates 6 electrons, total from 2 π-C₅H₅ = 2 × 6 = 12
- Oxidation state of Fe = +2
- EAN = 26 + 12 - 2 = 36 (Noble gas configuration)
- **Obeys EAN rule.**

3. **Count the compounds that obey the EAN rule:**
- Compounds that obey the EAN rule: (a), (e), (g)
- Total = 3

### Final Answer:
**3 of the given coordination compounds obey Sidgwick's EAN rule.**