One unified atomic mass unit represents a mass of magnitude

Options

A. `10^(-30)kg`
B. `1.66xx10^(27)kg`
C. `1.66xx10^(-27)kg`
D. `10^(30)kg`

Answer

To determine the mass represented by one unified atomic mass unit (AMU), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of AMU**:
One unified atomic mass unit (1 AMU) is defined as one twelfth (1/12) of the mass of one atom of the carbon-12 isotope (C-12).

2. **Mass of Carbon-12**:
The molar mass of carbon-12 is 12 grams per mole. This means that one mole of C-12 contains 12 grams of carbon.

3. **Avogadro's Number**:
One mole of any substance contains Avogadro's number of atoms, which is approximately \(6.022 \times 10^{23}\) atoms.

4. **Calculate the Mass of One Carbon-12 Atom**:
To find the mass of a single C-12 atom, we divide the total mass of one mole of C-12 by Avogadro's number:
\[ \text{Mass of one C-12 atom} = \frac{12 \text{ grams}}{6.022 \times 10^{23} \text{ atoms}}. \]

5. **Perform the Calculation**:
\[ \text{Mass of one C-12 atom} \approx \frac{12}{6.022 \times 10^{23}} \text{ grams} \approx 1.993 \times 10^{-23} \text{ grams}. \]

6. **Calculate 1 AMU**:
Since 1 AMU is defined as one twelfth of the mass of a C-12 atom, we calculate:
\[ 1 \text{ AMU} = \frac{1}{12} \times \text{Mass of one C-12 atom} = \frac{1}{12} \times 1.993 \times 10^{-23} \text{ grams}. \]

7. **Final Calculation**:
\[ 1 \text{ AMU} \approx \frac{1.993 \times 10^{-23}}{12} \approx 1.66 \times 10^{-27} \text{ grams}. \]

### Conclusion:
Thus, one unified atomic mass unit (1 AMU) represents a mass of approximately \(1.66 \times 10^{-27}\) grams.

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