Answer
$a = 3.42 \times 10^9 m/s^2$
Work Step by Step
When $r = 2.00R$, the electron is outside the shell, so the charge of the spherical metal shell is
$Q = 4 \pi R^2 \sigma $
And the net force is
$F = k \frac{Q|e|}{r^2} $
$F = k \frac{4 \pi R^2 \sigma|e|}{(2.00R)^2} $
$F = k \frac{4 \pi R^2 \sigma|e|}{4.00R^2} $
$F = k \pi \sigma|e|$
$F = (8.99 \times 10^9 N . m^2 / C^2) \pi (6.90 \times 10^{-13} C/m^2)(1.6 \times 10^{-19}C)$
$F = 3.12 \times 10^{-21} N$
According to Newton's Second Law of motion, acceleration can be calculated by
$F = ma$
$a = \frac{F}{m}$
$a = \frac{3.12 \times 10^{-21} N}{9.11 \times 10^{-31} kg }$
$a = 3.42 \times 10^9 m/s^2$
