Express unified atomic mass unit in kg.

Options

A. `1.66xx10^(-25)kg`
B. `1.66xx10^(-27)kg`
C. `1.66xx10^(-29)kg`
D. `1.66xx10^(-31)kg`

Explanation

To express the unified atomic mass unit (u or amu) in kilograms, we can follow these steps:

### Step 1: Understand the Definition of Atomic Mass Unit
The atomic mass unit is defined as one twelfth of the mass of a carbon-12 atom. This means that:
\[ 1 \, \text{amu} = \frac{1}{12} \times \text{mass of carbon-12 atom} \]

### Step 2: Find the Mass of Carbon-12 Atom
The mass of a carbon-12 atom is approximately:
\[ \text{Mass of carbon-12 atom} = 1.992647 \times 10^{-26} \, \text{kg} \]

### Step 3: Calculate the Atomic Mass Unit in Kilograms
Now, we can substitute the mass of the carbon-12 atom into the equation for the atomic mass unit:
\[ 1 \, \text{amu} = \frac{1}{12} \times 1.992647 \times 10^{-26} \, \text{kg} \]

### Step 4: Perform the Calculation
Calculating the above expression:
\[ 1 \, \text{amu} = \frac{1.992647 \times 10^{-26}}{12} \]
\[ 1 \, \text{amu} = 1.66056 \times 10^{-27} \, \text{kg} \]

### Step 5: Round the Result
For simplicity, we can round the result to:
\[ 1 \, \text{amu} \approx 1.66 \times 10^{-27} \, \text{kg} \]

### Conclusion
Thus, the unified atomic mass unit (amu) is approximately:
\[ 1 \, \text{amu} \approx 1.66 \times 10^{-27} \, \text{kg} \]

### Final Answer
Therefore, 1 unified atomic mass unit is equal to \( 1.66 \times 10^{-27} \, \text{kg} \).

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