# Why am I failing to calculate the Bohr radius correctly? [closed]

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?
• Your formula misses a factor $4\pi\epsilon_0$. See en.wikipedia.org/wiki/Bohr_radius Oct 28 at 6:35
• @ThomasFritsch If you post this as an answer, I'll accept it as the answer to my question. Thanks for your reply! Oct 28 at 6:59

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