What is energy equivalent to a `10 mug` mass?

Options

A. `9xx 10^(8)J`
B. `3xx 10^(11)J`
C. `5xx 10^(11)J`
D. `7xx 10^(-11)J`

Answer

To find the energy equivalent to a mass of 10 micrograms, we can use Einstein's mass-energy equivalence formula, which is given by:

\[ E = mc^2 \]

where:
- \( E \) is the energy,
- \( m \) is the mass,
- \( c \) is the speed of light in a vacuum (approximately \( 3 \times 10^8 \) m/s).

### Step 1: Convert the mass from micrograms to kilograms
Given mass:
\[ 10 \text{ micrograms} = 10 \times 10^{-6} \text{ grams} \]

To convert grams to kilograms:
\[ 10 \times 10^{-6} \text{ grams} = 10 \times 10^{-6} \times 10^{-3} \text{ kg} = 10 \times 10^{-9} \text{ kg} = 10^{-8} \text{ kg} \]

### Step 2: Substitute the mass into the energy equation
Now we can substitute the mass into the energy equation \( E = mc^2 \):
\[ E = (10^{-8} \text{ kg}) \times (3 \times 10^8 \text{ m/s})^2 \]

### Step 3: Calculate \( c^2 \)
Calculating \( c^2 \):
\[ c^2 = (3 \times 10^8)^2 = 9 \times 10^{16} \text{ m}^2/\text{s}^2 \]

### Step 4: Substitute \( c^2 \) back into the energy equation
Now substitute \( c^2 \) back into the equation:
\[ E = 10^{-8} \text{ kg} \times 9 \times 10^{16} \text{ m}^2/\text{s}^2 \]

### Step 5: Perform the multiplication
Calculating the energy:
\[ E = 9 \times 10^{8} \text{ joules} \]

### Final Answer
Thus, the energy equivalent to a mass of 10 micrograms is:
\[ E = 9 \times 10^8 \text{ joules} \]