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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?
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    $\begingroup$ Your formula misses a factor $4\pi\epsilon_0$. See en.wikipedia.org/wiki/Bohr_radius $\endgroup$ Oct 28 at 6:35
  • $\begingroup$ @ThomasFritsch If you post this as an answer, I'll accept it as the answer to my question. Thanks for your reply! $\endgroup$ Oct 28 at 6:59
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Your formula misses a factor $4\pi\epsilon_0$. According to Wikipedia - Bohr radius the correct formula is $$r_n=\frac{4\pi\epsilon_0h^2}{4\pi^2me^2}\times\frac{n^2}{Z}$$

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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.

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