One atomic mass unit in kilogram is

Options

A. `1//N_(A)`
B. `12//N_(A)`
C. `1//1000 N_(A)`
D. `1000//N_(A)`

Answer

To find the value of one atomic mass unit (amu) in kilograms, we can follow these steps:

### Step-by-Step Solution:

1. **Definition of Atomic Mass Unit (amu)**:
- One atomic mass unit (1 amu) is defined as \( \frac{1}{12} \) of the mass of a carbon-12 atom.

2. **Expressing 1 amu in grams**:
- Therefore, we can express 1 amu in grams as:
\[ 1 \text{ amu} = \frac{1}{12} \times 12 \text{ g} = \frac{12 \text{ g}}{N_a} \]
where \( N_a \) is Avogadro's number, approximately \( 6.022 \times 10^{23} \).

3. **Converting grams to kilograms**:
- Since we need to convert this value into kilograms, we know that:
\[ 1 \text{ kg} = 1000 \text{ g} \]
- Therefore, we can convert grams to kilograms by dividing by 1000:
\[ 1 \text{ amu} = \frac{12 \text{ g}}{N_a \times 1000} \]

4. **Final Expression**:
- Thus, we can express 1 amu in kilograms as:
\[ 1 \text{ amu} = \frac{1}{1000 N_a} \text{ kg} \]
- Substituting the value of \( N_a \):
\[ 1 \text{ amu} \approx \frac{1}{1000 \times 6.022 \times 10^{23}} \text{ kg} \]

5. **Calculating the Numerical Value**:
- To find the numerical value:
\[ 1 \text{ amu} \approx 1.660539 \times 10^{-27} \text{ kg} \]

### Conclusion:
Thus, one atomic mass unit (1 amu) is approximately \( 1.660539 \times 10^{-27} \) kg.

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