Why am I failing to calculate the Bohr radius correctly?

Question

This is the formula that I'm using:

$$r_n=\frac{h^2}{4\pi^2me^2}\times\frac{n^2}{Z}$$

Here,

$r_n$ = radius of nth orbit

$h$ = Planck's constant $(6.626\times10^{-34}Js)$

$m$ = mass of an electron $(9.1\times10^{-31}kg)$

$e$ = charge of a proton $(1.6\times10^{-19}C)$

$n$ = principal quantum number ($n=1$ in our case)

$Z$ = atomic number

My attempt:

$$r_1=\frac{(6.626\times10^{-34})^2}{4\pi^2\times9.1\times10^{-31}\times(1.6\times10^{-19})^2}\times\frac{1}{1}$$

$$=0.477m\ (\text{approx})$$

But this is the wrong answer! The correct Bohr radius is $0.0529\times10^{-9}m$

Question:

1. Why am I getting the wrong answer? What mistake am I making?

Answer 1

Your formula misses a factor $4\pi\epsilon_0$. According to Wikipedia - Bohr radius the correct formula is $$r_n=\frac{4\pi\epsilon_0h^2}{4\pi^2me^2}\times\frac{n^2}{Z}$$

Answer 2

Your mathematical calculation is correct, but your formula is not correct and you didn't take into account the reduced mass of proton - electron see StackExchange answer and Wikipedia.