Two small silver spheres, each with a mass of 8.00 g, are separated by 1.00 m. C

Question

Two small silver spheres, each with a mass of 8.00 g, are separated by 1.00 m. Calculate the fraction of the electrons in one sphere that must be transferred to the other to produce an attracts force of 1 00 x 10^4 N (about 1 ton) between the spheres. (The number of electrons per atom of Silver is 47, and the number of atoms per gram is Avogadro's number divided by the molar mass of silver, 107.87 g/mol.) The figure below shows the electric field lines for two charged particles separated by a small distance.

Explanation / Answer

Let magnitude of charge on each sphere be Q coulomb
F = K*Q*Q/r^2
1*10^4 = (9*10^9)*Q^2 / 1^2
Q = 1.054*10^-3 C

number of electron transferred = Q / charge of 1 electron
= (1.054*10^-3) / (1.6*10^-19)
= 6.59*10^15 electron

Let us now find the total number of electron present
Number of moles of silver = mass / molar mass
= 8/107.87
= 0.074 mol

Number of atom = number of mol * 6.022*10^23
= 0.074*(6.022*10^23)
= 4.466*10^22

Total number of electron = number of atom * 47
= 4.466*10^22 * 47
= 2.099*10^24

fraction of electron transferred = (6.59*10^15 ) / 2.099*10^24
= 3.14*10^-9
Answer: 3.14*10^-9

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