Question

what is the energy equivalent of an object with a mass of 1.05 g?
○ 3.15 × 10⁵ j
○ 3.15 × 10⁸ j
○ 9.45 × 10¹³ j
○ 9.45 × 10¹⁶ j

Explanation:

Step1: Recall Einstein's mass - energy equivalence formula

The formula for mass - energy equivalence is \(E = mc^{2}\), where \(E\) is the energy, \(m\) is the mass, and \(c\) is the speed of light in a vacuum (\(c=3.0\times 10^{8}\space m/s\)).

Step2: Convert the mass to kilograms

The mass \(m = 1.05\space g\). Since \(1\space kg=1000\space g\), we convert grams to kilograms by dividing by 1000. So \(m=\frac{1.05}{1000}\space kg = 1.05\times 10^{- 3}\space kg\).

Step3: Substitute the values into the formula

Substitute \(m = 1.05\times 10^{-3}\space kg\) and \(c = 3.0\times 10^{8}\space m/s\) into \(E=mc^{2}\).
\[

$$\begin{align*} E&=(1.05\times 10^{-3}\space kg)\times(3.0\times 10^{8}\space m/s)^{2}\\ &=(1.05\times 10^{-3})\times(9.0\times 10^{16})\space J\\ &=(1.05\times9.0)\times 10^{-3 + 16}\space J\\ &=9.45\times 10^{13}\space J \end{align*}$$

\]

Answer:

\(9.45\times 10^{13}\space J\) (the option with \(9.45\times 10^{13}\space J\))