Final answer:
The energy absorbed during the fusion process that increased the mass from 1.58 x 10⁻⁶ kg to 2.019 x 10⁻⁶ kg is calculated using the change in mass and Einstein's equation (E = mc²), resulting in 3.947 x 10⁻⁰ Joules of energy absorbed.
Step-by-step explanation:
The student is asking about the amount of energy absorbed when the mass of a substance is increased via fusion. To solve this, we need to calculate the change in mass (Δm) and then use Einstein's equation E = mc² to determine the energy absorbed. The initial mass is 1.58 x 10⁻⁶ kg, and the final mass after fusion is 2.019 x 10⁻⁶ kg. So, the change in mass is:
Δm = (2.019 - 1.58) x 10⁻⁶ kg = 0.439 x 10⁻⁶ kg
Now, we use the speed of light c = 2.99792458 x 10⁸ m/s:
E = Δmc² = (0.439 x 10⁻⁶ kg) x (2.99792458 x 10⁸ m/s)²
Calculating the energy in Joules, we get:
E = 0.439 x 10⁻⁶ kg x (8.987551787 x 10ⁱ⁶ m²/s²) = 3.947 x 10⁻⁰ J
This energy represents the energy absorbed during the fusion process.