Two positive ions , each carrying a charge `q` , are separated by a distance `d`.If `F` is the force of repulsion between the ions , the number of electrons missing from each ion will be (`e` being the charge on an electron)

Options

A. `(4pi epsilon_(0)Fd^(2))/(e^(2))`
B. `sqrt((4pi epsilon_(0)Fe^(2))/(d^(2)))`
C. `sqrt((4pi epsilon_(0)Fe^(2))/(e^(2)))`
D. `(4pi epsilon_(0)Fd^(2))/(q^(2))`

Answer

C

Explanation

According to Coulomb.s law , the force of repultion between the two positive ions each of charge q, separated by a distance d given by
`F = (1)/(4pi epsilon_(0))((q)(q))/(d^(2)) , F = (q^(2))/(4pi epsilon_(0) d^(2)), q^(2) = 4pi epsilon_(0) Fd^(2)`
`q = sqrt(4pi epsilon_(0) Fd^(2))`
Since, q = ne
where n = number of electrons missing from each ion
e = magnitude of charge on electron
`:. n=(q)/(e) = sqrt((4pi epsilon_(0)Fd^(2))/(e^(2)))` (Using (i))