1 a.m.u is equivalent to

Options

A. `1.6xx10^(-12)`joule
B. `1.6xx10^(-19)` joule
C. `1.5xx10^(-10)` joule
D. `1.5xx10^(-19)` joule

Answer

To find the equivalent of 1 atomic mass unit (amu) in joules, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of amu**:
- An atomic mass unit (amu) is defined as one twelfth of the mass of a carbon-12 atom.

2. **Calculate the Mass of 1 amu in grams**:
- Since 1 mole of carbon-12 weighs 12 grams and contains Avogadro's number of atoms (approximately \(6.022 \times 10^{23}\)), the mass of one carbon-12 atom is:
\[ \text{Mass of 1 atom} = \frac{12 \text{ grams}}{6.022 \times 10^{23}} \approx 1.99 \times 10^{-24} \text{ grams} \]
- Therefore, 1 amu is approximately \(1.66 \times 10^{-24}\) grams.

3. **Convert grams to kilograms**:
- To convert grams to kilograms, we divide by 1000:
\[ 1 \text{ amu} = 1.66 \times 10^{-24} \text{ grams} = 1.66 \times 10^{-27} \text{ kg} \]

4. **Use Einstein's equation to find energy**:
- According to Einstein's equation \(E = mc^2\), where \(c\) is the speed of light (\(3 \times 10^8 \text{ m/s}\)):
\[ E = (1.66 \times 10^{-27} \text{ kg}) \times (3 \times 10^8 \text{ m/s})^2 \]
- Calculate \(c^2\):
\[ c^2 = (3 \times 10^8)^2 = 9 \times 10^{16} \text{ m}^2/\text{s}^2 \]

5. **Calculate the energy in joules**:
- Now substitute \(c^2\) back into the energy equation:
\[ E = 1.66 \times 10^{-27} \text{ kg} \times 9 \times 10^{16} \text{ m}^2/\text{s}^2 \]
\[ E \approx 1.494 \times 10^{-10} \text{ joules} \]

6. **Final Result**:
- Therefore, we can conclude that:
\[ 1 \text{ amu} \approx 1.5 \times 10^{-10} \text{ joules} \]