The equivalent energy of 1 g of substance is

Options

A. `9xx10^13` J
B. `6xx10^12` J
C. `3xx10^13` J
D. `6xx10^13` J

Explanation

To find the equivalent energy of 1 gram of substance using Einstein's mass-energy relation, we can follow these steps:

### Step 1: Understand the Mass-Energy Relation
Einstein's mass-energy relation is given by the formula:
\[ E = mc^2 \]
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 2: Convert Mass from Grams to Kilograms
Since the standard unit of mass in the SI system is kilograms, we need to convert 1 gram to kilograms:
\[ 1 \text{ gram} = \frac{1}{1000} \text{ kg} = 0.001 \text{ kg} \]

### Step 3: Substitute Values into the Formula
Now, we can substitute the values into the mass-energy relation:
- Mass \( m = 0.001 \text{ kg} \)
- Speed of light \( c = 3 \times 10^8 \text{ m/s} \)

Substituting these values into the equation:
\[ E = (0.001 \text{ kg}) \times (3 \times 10^8 \text{ m/s})^2 \]

### Step 4: Calculate \( c^2 \)
First, calculate \( c^2 \):
\[ c^2 = (3 \times 10^8)^2 = 9 \times 10^{16} \text{ m}^2/\text{s}^2 \]

### Step 5: Calculate the Energy
Now substitute \( c^2 \) back into the energy formula:
\[ E = 0.001 \text{ kg} \times 9 \times 10^{16} \text{ m}^2/\text{s}^2 \]
\[ E = 9 \times 10^{13} \text{ kg m}^2/\text{s}^2 \]
Since \( 1 \text{ kg m}^2/\text{s}^2 = 1 \text{ Joule} \), we have:
\[ E = 9 \times 10^{13} \text{ Joules} \]

### Final Answer
The equivalent energy of 1 gram of substance is:
\[ \boxed{9 \times 10^{13} \text{ Joules}} \]

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