In one model of the electron, the electron of mass me is thought to be a uniformly charged shell of radius R and total charge e, whose electrostatic energy E is equivalent to its mass me via Einstein's mass energy relation `E = m_(e)c^(2)`. In this model, R is approximately (`m_(e) = 9.1 xx 10^(-31) kg, c = 3 xx 10^(8), 1//4 pi epsilon_(0) = 9 xx 10^(9) "Farad" m^(-1)` , magnitude of the electron charge `= 1.6 xx 10^(-19)C`) –

Options

A. `1.4 xx 10^(-15)m`
B. `2 xx 10^(-13)m`
C. `5.3 xx 10^(-11)m`
D. `2.8 xx 10^(-35)m`

Answer

A

Explanation

`U= mc^(2) rArr (KQ^(2))/(2R) = mc^(2) rArr (9 xx 10^(9) xx (1.6 xx 10^(-19))^(2))/(2R) = 9.1 xx 10^(-31) xx (3 xx 10^(8))^(2)`
`R= (9 xx 10^(9) xx (1.6 xx 10^(-19))^(2))/(2 xx 9.1 xx 10^(-31) xx (3 xx 10^(8))^(2))= 1.4 xx 10^(-15) m`