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.

Respuesta :

Answer:

4.60 × 10⁻⁸

Explanation:

From the given information;

Assuming that q charges are transferred, then:

[tex]F = \dfrac{kq^2}{d^2}[/tex]

where;

k = 9 ×10⁹

[tex]900000 = \dfrac{9*10^9 \times q^2}{1.2^2}[/tex]

[tex]q = \sqrt{\dfrac{900000\times 1.2^2 }{9*10^9}}[/tex]

q = 0.012 C

No of the electrons transferred is:

[tex]= \dfrac{0.012}{1.6\times 10^{-19}} C[/tex]

[tex]= 7.5 \times 10^{16} \ C[/tex]

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

here;

[tex]\text{ no of moles }= \dfrac{6.2}{107.87}[/tex]

no of moles = 0.0575 mol

Initial number of electrons =  [tex]6.023\times 10^{23} \times 47 \times 0.0575 mol[/tex]

= 1.63 × 10²⁴

The fraction of electrons transferred  [tex]=\dfrac{7.5\times 10^{16} }{1.6 3\times 10^{24}}[/tex]

= 4.60 × 10⁻⁸