Could someone check my answer?
Q. Assume an arbitrary atom X with atomic number (nuclear charge) of Z. Calculate
the maximum possible value of Z which an ion X^+(Z-1)
can have keeping in mind
that the electron cannot move faster than the speed of light (we already know that
the maximum achievable speed is the speed of light). Ignore the relativistic effects
and use Bohr model concepts to solve this problem.

Question

Could someone check my answer?
Q. Assume an arbitrary atom X with atomic number (nuclear charge) of Z. Calculate
the maximum possible value of Z which an ion X^+(Z-1)
can have keeping in mind
that the electron cannot move faster than the speed of light (we already know that
the maximum achievable speed is the speed of light). Ignore the relativistic effects
and use Bohr model concepts to solve this problem.

anonymous · Answer

I used the following formula to calculate Z.
$$v=\frac{ Z e ^{2} }{ 2n \epsilon h}$$
I got the answer for Z= 137. 
Am I  doing this correctly?