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A carbon-12 atom has a mass defect of 0.09564 amu.

Which setup is used to calculate nuclear binding energy?

A. [tex]\(0.09564 \, \text{amu} \times \left(1.6606 \times 10^{-27} \, \text{kg} \right) / \text{amu} \times \left(3.0 \times 10^8\right)^2\)[/tex]

B. [tex]\(0.09564 \, \text{amu} \times 1 \, \text{amu} / \left(1.6606 \times 10^{-27} \, \text{kg} \right) \times \left(3.0 \times 10^8\right)^2\)[/tex]

C. [tex]\(0.09564 \, \text{amu} \times \left(3.0 \times 10^8\right)^2\)[/tex]

D. [tex]\(0.09564 \, \text{amu} \times \left(1.6606 \times 10^{-27} \, \text{kg} \right) / \text{amu} \times \left(3.0 \times 10^8\right)\)[/tex]

Sagot :

GinnyAnswer
To find the nuclear binding energy based on the given mass defect, we need to use Einstein's mass-energy equivalence formula, which is [tex]\(E = mc^2\)[/tex].

Here the steps are:

1. Convert the mass defect from atomic mass units (amu) to kilograms (kg):
We use the conversion factor [tex]\(1.6606 \times 10^{-27} \text{ kg/amu}\)[/tex] to convert the mass defect.
[tex]\[\text{Mass defect in kg} = 0.09564 \text{ amu} \times 1.6606 \times 10^{-27} \text{ kg/amu}\][/tex]

2. Square the speed of light:
The speed of light ([tex]\(c\)[/tex]) is [tex]\(3.0 \times 10^8 \text{ m/s}\)[/tex].
[tex]\[c^2 = (3.0 \times 10^8 \text{ m/s})^2\][/tex]

3. Multiply the converted mass defect by the square of the speed of light:
This gives us the nuclear binding energy.
[tex]\[\text{Nuclear binding energy} = (\text{mass defect in kg}) \times c^2\][/tex]

Putting it all together, the correct setup is:
[tex]\[0.09564 \text{ amu} \times \left(1.6606 \times 10^{-27} \text{ kg}\right) / \text{amu} \times \left(3.0 \times 10^8 \text{ m/s}\right)^2\][/tex]

So, the correct setup to calculate the nuclear binding energy is:
[tex]\[0.09564 \text{ amu} \times \left(1.6606 \times 10^{-27} \text{ kg}\right) / \text{amu} \times \left(3.0 \times 10^8 \text{ m/s}\right)^2\][/tex]
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