Question

Two small silver spheres, each of mass m=6.2 g, are separated by distance d=1.2 m. As a result of transfer of some fraction of electrons from one sphere to the other, there is an attractive force F=900 KN between the spheres. Calculate the fraction of electrons transferred from one of the spheres: __________

To evaluate the total number of electrons in a silver sphere, you will need to invoke Avogadro's number, the molar mass of silver equal to 107.87 g/mol and the fact that silver has 47 electrons per atom.

Answer 1

4.60 × 10⁻⁸

Step-by-step explanation:

From the given information;

Assuming that q charges are transferred, then:

`F = (kq^2)/(d^2)`

where;

k = 9 ×10⁹

`900000 = (9*10^9 * q^2)/(1.2^2)`

`q = \sqrt{(900000* 1.2^2 )/(9*10^9)}`

q = 0.012 C

No of the electrons transferred is:

`= (0.012)/(1.6* 10^(-19)) C`

`= 7.5 * 10^(16) \ C`

Initial number of electrons = N × 47 × no of moles

here;

`\text{ no of moles }= (6.2)/(107.87)`

no of moles = 0.0575 mol

∴

Initial number of electrons =
`6.023* 10^(23) * 47 * 0.0575 mol`

= 1.63 × 10²⁴

The fraction of electrons transferred
`=(7.5* 10^(16) )/(1.6 3* 10^(24))`

= 4.60 × 10⁻⁸