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The centripetal force is given by:

#F=(mv^2)/r# as stated (where m is the mass of the electron):

We have been told that:

#m=9.1times10^(-31)kg#
#v=2.1113times10^(6)ms^(-1)#
#r=5.2335times10^(-11)m#

Simply put these numbers into the expression to find the force:

#F=(mv^2)/r=((9.1times10^(-31))(2.1113times10^(6))^2)/(5.2335times10^(-11))#

#=7.7509times10^(-8)N#

For the electrostatic force use:

#F=(Q_1Q_2)/(4piepsilon_o r^2)#

In the case:

The charge of the electron is the same but opposite the charge of the neutron so (we want the magnitude so just take the positive of both anyway):

#Q_1=Q_2=1.6times10^(-19)C#

#epsilon# is the permittivity of free space:

#epsilon= 8.854times10^(-12)#

Finally, #r# is the radius again:

#r=5.2335times10^(-11)m#

Plug these into the formula to get:

#F=(Q_1Q_2)/(4piepsilon_o r^2)=((1.6times10^(-19))(1.6times10^(-19)))/(4pi(8.854times10^(-12))(5.2335times10^(-11))^2)#

#8.4005times10^(-8)N#

There are discrepancies in the results (e.g. the two forces are out by about #0.65times10^(-8)N#. This may be due to assuming a circular orbit. A modified version of the bohr model assumes an elliptical orbit which means the velocity, radius and force don't stay constant.

Any further discrepancies may also may be down to the fact that relativistic effects have not been accounted for.

My calculations are as follows:

#F_c = (mv^2)/r = (9.1xx10^-31xx(2.1113xx10^6)^2)/(5.2335xx10^-11)#

#F_c = 7.748xx10^-8#N

#F_e = (1/(4piepsilon_0))((q_1q_2)/r^2) #

#F_e = 1/(4pixx8.85xx10^-12)((1.6xx10^-19)^2/(5.2335xx10^-11)^2)#

#F_e = 8.404xx10^-8#N