how energy can be negative as energy of electron is [-13.6z2/n2]ev?

Here -ve sign only means that the electron is bound by some attractive force As the force on electron = -(kq1q2)/r2 where q1 is charge of nucleus and q2 magnitude of charge of electron as sign is already taken. Where k =1/(4pi epsilon not) Hence potential energy associated is integral of -F.dr I.e. U=-(kq1q2)/r where k is the same You can also think a reason for -ve sign like this Suppose an electron experiencing attractive force by nucleus and it has some initial potential energy (+ve or -ve ) Now you pull the electron to infinity so that now no force is experienced by your electron. In this process final energy of the electron is zero(because of no interacting force at the final state) also you know that you did the positive work in taking the electron to infinity .(displacement is in direction of force) and most importantly (work done by external agent is stored in form of its potential energy). hence final potential energy must have increased but you know that final energy is zero .so initial energy must be some negative quantity.........!