You Can Run, But You Can't Escape

Consider an electron taken as the size of the Earth. On this 'planet', let the escape velocity be $v_e$ , where $v_e=a\times 10^{13}$ ms $^{-1}$ . Find $\lfloor a\rfloor$

Details and Assumptions:

• Electron's density $=2.17\times10^{14}$ g cm $^{-3}$

• Radius of the earth $=6371$ km

• Consider the Earth as spherical, and homogenous, if necessary

• Neglect electrostatic forces