what is the nuclear binding energy of an atom that has a mass defect of 1.643×10⁻²⁸ kg? use e = mc²…

what is the nuclear binding energy of an atom that has a mass defect of 1.643×10⁻²⁸ kg? use e = mc². (remember: the speed of light is approximately 3.00×10⁸ m/s.)\n1.83×10⁻⁴⁶ j\n4.93×10⁻²⁰ j\n1.48×10⁻¹¹ j\n5.48×10⁴⁵ j

what is the nuclear binding energy of an atom that has a mass defect of 1.643×10⁻²⁸ kg? use e = mc². (remember: the speed of light is approximately 3.00×10⁸ m/s.)\n1.83×10⁻⁴⁶ j\n4.93×10⁻²⁰ j\n1.48×10⁻¹¹ j\n5.48×10⁴⁵ j

Answer

Explanation:

Step1: Identify values

$m = 1.643\times10^{-28}\text{ kg}$, $c = 3.00\times10^{8}\text{ m/s}$

Step2: Substitute into formula

$E=mc^{2}=(1.643\times 10^{-28})\times(3.00\times 10^{8})^{2}$

Step3: Calculate $(3.00\times 10^{8})^{2}$

$(3.00\times 10^{8})^{2}=3.00^{2}\times(10^{8})^{2}=9.00\times10^{16}$

Step4: Multiply by mass

$E=(1.643\times 10^{-28})\times(9.00\times10^{16})=(1.643\times9.00)\times10^{-28 + 16}$ $E = 14.787\times10^{-12}=1.4787\times 10^{-11}\approx1.48\times 10^{-11}\text{ J}$

Answer:

$1.48\times 10^{-11}\text{ J}$ (corresponding to the third option)