The number of neutrons in a drop water `(20 drops =1 mL)` at `4^(@)C`

Options

A. `6.023 xx 10^(22)`
B. `1.338 xx 10^(22)`
C. `6.023 xx 10^(20)`
D. `7.338 xx 10^(22)`

Answer

To find the number of neutrons in a drop of water at 4°C, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the Volume of One Drop of Water**:
Given that 20 drops of water equal 1 mL, the volume of one drop is:
\[ \text{Volume of one drop} = \frac{1 \text{ mL}}{20} = 0.05 \text{ mL} \]

**Hint**: Remember that 1 mL is equivalent to 1 cm³.

2. **Calculate the Mass of One Drop of Water**:
The density of water is approximately 1 g/mL. Therefore, the mass of one drop of water is:
\[ \text{Mass of one drop} = \text{Density} \times \text{Volume} = 1 \text{ g/mL} \times 0.05 \text{ mL} = 0.05 \text{ g} \]

**Hint**: Density is defined as mass per unit volume.

3. **Calculate the Number of Moles of Water in One Drop**:
The molar mass of water (H₂O) is approximately 18 g/mol. The number of moles in one drop is calculated as:
\[ \text{Number of moles} = \frac{\text{Mass}}{\text{Molar mass}} = \frac{0.05 \text{ g}}{18 \text{ g/mol}} = \frac{0.05}{18} \text{ moles} \]

**Hint**: Moles can be calculated using the formula: moles = mass / molar mass.

4. **Determine the Number of Neutrons in One Mole of Water**:
Water (H₂O) consists of 2 hydrogen atoms and 1 oxygen atom. Hydrogen has 0 neutrons, and oxygen has 8 neutrons (mass number 16 - atomic number 8). Therefore, the total number of neutrons in one mole of water is:
\[ \text{Total neutrons in 1 mole of H₂O} = 2 \times 0 + 1 \times 8 = 8 \text{ neutrons} \]

**Hint**: Neutrons can be found by subtracting the number of protons (atomic number) from the mass number.

5. **Calculate the Total Number of Neutrons in One Drop of Water**:
The number of neutrons in the amount of water in one drop is:
\[ \text{Number of neutrons in one drop} = \text{Number of moles} \times \text{Number of neutrons per mole} \]
\[ = \left(\frac{0.05}{18}\right) \text{ moles} \times 8 \text{ neutrons/mole} = \frac{0.05 \times 8}{18} = \frac{0.4}{18} \text{ neutrons} \]

**Hint**: Multiply the number of moles by the number of neutrons per mole to find the total.

6. **Convert to Number of Neutrons**:
To find the total number of neutrons, we multiply by Avogadro's number (approximately \(6.022 \times 10^{23}\)):
\[ \text{Total neutrons} = \frac{0.4}{18} \times 6.022 \times 10^{23} \approx 1.338 \times 10^{20} \text{ neutrons} \]

**Hint**: Avogadro's number is used to convert moles to individual particles.

### Final Answer:
The number of neutrons in a drop of water at 4°C is approximately \(1.338 \times 10^{20}\) neutrons.