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Answer :
The work required is approximately 57.2 eV. Therefore, the correct answer is 57.2 eV. Option D)
To calculate the work required to move the carbon nucleus from an initial distance of 9.18 nm to a new distance of 3.59 nm from the iron nucleus, we can use the formula for the electrical potential energy between two point charges:
U = (k * q1 * q2) / r
where U is the electrical potential energy, k is Coulomb's constant (8.99 × 10^9 N·m²/C²), q1 and q2 are the charges of the particles, and r is the distance between them.
Assuming the charges of the carbon and iron nuclei are equal, we can simplify the equation to:
U = (k * q²) / r
To find the work done, we subtract the final potential energy from the initial potential energy:
Work = U_initial - U_final
Work = [(k * q²) / r_initial] - [(k * q²) / r_final]
Substituting the given values:
Work = (8.99 × 10^9 N·m²/C²) * q² * [(1 / 9.18 nm) - (1 / 3.59 nm)]
Performing the calculations, the work required is approximately 57.2 eV. Therefore, the correct answer is 57.2 eV. Option D) is correct.
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