The nuclear reaction `(s)` accompanied with the emission of neutron`(s)` is `//` are

Options

A. `._(13)Al^(17)+._(2)He^(4)rarr ._(15)P^(30)`
B. `._(6)C^(12)+._(1)He^(1) rarr._(7)N^(13)`
C. `._(15)P^(30)rarr ._(14)Si^(30)+._(1)e^(0)`
D. `._(96)Am^(241)+._(2)He^(4)rarr ._(97)Bk^(244)+._(1)e^(0)`

Explanation

To determine which nuclear reactions are accompanied by the emission of neutrons, we will analyze each option by comparing the mass numbers and atomic numbers of the reactants and products.

### Step-by-Step Solution:

1. **Option 1: Aluminium Bombarded with Helium**
- Reactants: Aluminium (mass number 27, atomic number 13) + Helium (mass number 4, atomic number 2)
- Products: Phosphorus (mass number 30, atomic number 15) + Neutron
- Calculate the total mass number and atomic number for reactants:
- Mass number: 27 (Al) + 4 (He) = 31
- Atomic number: 13 (Al) + 2 (He) = 15
- Calculate the total mass number and atomic number for products:
- Mass number: 30 (P) + 1 (Neutron) = 31
- Atomic number: 15 (P) = 15
- Conclusion: Mass numbers are equal, atomic numbers are equal, indicating emission of a neutron.

2. **Option 2: Carbon Bombarded with Proton**
- Reactants: Carbon (mass number 12, atomic number 6) + Proton (mass number 1, atomic number 1)
- Products: Nitrogen (mass number 13, atomic number 7)
- Calculate the total mass number and atomic number for reactants:
- Mass number: 12 (C) + 1 (P) = 13
- Atomic number: 6 (C) + 1 (P) = 7
- Calculate the total mass number and atomic number for products:
- Mass number: 13 (N) = 13
- Atomic number: 7 (N) = 7
- Conclusion: Mass numbers and atomic numbers are equal, indicating no emission of a neutron.

3. **Option 3: Phosphorus Decaying to Silicon**
- Reactants: Phosphorus (mass number 30, atomic number 15)
- Products: Silicon (mass number 30, atomic number 14) + Positron
- Calculate the total mass number and atomic number for reactants:
- Mass number: 30 (P) = 30
- Atomic number: 15 (P) = 15
- Calculate the total mass number and atomic number for products:
- Mass number: 30 (Si) + 0 (Positron) = 30
- Atomic number: 14 (Si) + 1 (Positron) = 15
- Conclusion: Mass numbers and atomic numbers are equal, indicating no emission of a neutron.

4. **Option 4: Americium Bombarded with Helium**
- Reactants: Americium (mass number 241, atomic number 96) + Helium (mass number 4, atomic number 2)
- Products: Berkelium (mass number 244, atomic number 97) + Positron
- Calculate the total mass number and atomic number for reactants:
- Mass number: 241 (Am) + 4 (He) = 245
- Atomic number: 96 (Am) + 2 (He) = 98
- Calculate the total mass number and atomic number for products:
- Mass number: 244 (Bk) + 0 (Positron) = 244
- Atomic number: 97 (Bk) + 1 (Positron) = 98
- Conclusion: There is a difference in mass numbers, indicating emission of a neutron.

### Final Answer:
The nuclear reactions accompanied by the emission of neutrons are **Option 1 and Option 4**.