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Einstein's famous equation relating mass and energy is E=mc ^2 where c is the velocity of light (c=2.998×10 ^8 m/sec). Use this equation to calculate the energy equivalent of 1 amu.

User Shwetap
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Answer:

Approximately
1.495 * 10^(-10)\; {\rm J}.

Step-by-step explanation:

Atomic mass unit (
{\rm amu}) is a unit for mass. In standard unit, one atomic mass unit is equivalent to approximately
1.661 * 10^(-27)\; {\rm kg}.

Substitute
m \approx 1.661 * 10^(-27)\; {\rm kg} and
c \approx 2.998 * 10^(8)\; {\rm m\cdot s^(-1)} into the equation:


\begin{aligned}E &= m\, c^(2) \\ &\approx (1.661 * 10^(-27)\; {\rm kg})\, (3.00 * 10^(8)\; {\rm m\cdot s^(-1)})^(2) \\ &\approx 1.495 * 10^(-10)\; {\rm kg \cdot m^(2)\cdot s^(-2)}\end{aligned}.

Note that
1\; {\rm kg\cdot m^(2)\cdot s^(-2)} is equivalent to
1\; {\rm J} (one Joule.) Therefore, the energy equivalent to
1\; {\rm amu} would be approximately
1.495 * 10^(-10)\; {\rm J}.

User Faminator
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