the starting materials in a nuclear change have a total mass of 2.3465×10⁻²⁷ kg. after the change, the…

the starting materials in a nuclear change have a total mass of 2.3465×10⁻²⁷ kg. after the change, the resulting materials have a mass of 2.3148×10⁻²⁷ kg. how much energy was released during the change?\no 2.85×10⁻¹² j\no 2.08×10⁻¹⁰ j\no 2.11×10⁻¹⁰ j\no 8.56×10⁻⁴ j

the starting materials in a nuclear change have a total mass of 2.3465×10⁻²⁷ kg. after the change, the resulting materials have a mass of 2.3148×10⁻²⁷ kg. how much energy was released during the change?\no 2.85×10⁻¹² j\no 2.08×10⁻¹⁰ j\no 2.11×10⁻¹⁰ j\no 8.56×10⁻⁴ j

Answer

Explanation:

Step1: Calculate mass - defect

The mass - defect $\Delta m$ is the difference between the initial mass $m_i$ and the final mass $m_f$. $\Delta m=m_i - m_f=(2.3465\times 10^{-27}-2.3148\times 10^{-27})\text{ kg}=0.0317\times 10^{-27}\text{ kg}=3.17\times 10^{-29}\text{ kg}$

Step2: Use Einstein's mass - energy equivalence formula

Einstein's mass - energy equivalence formula is $E = \Delta mc^{2}$, where $c = 3\times 10^{8}\text{ m/s}$. $E=(3.17\times 10^{-29}\text{ kg})\times(3\times 10^{8}\text{ m/s})^{2}$ $E=(3.17\times 10^{-29})\times9\times 10^{16}\text{ J}$ $E = 28.53\times 10^{-13}\text{ J}=2.853\times 10^{-12}\text{ J}\approx2.85\times 10^{-12}\text{ J}$

Answer:

$2.85\times 10^{-12}\text{ J}$