Bohr model radius v/s calculated radius in periodic table in Hydrogen and Hydrogen-like substances

Jan 2020
Mumbai(Bombay), Maharashtra State, India.
Radius of Bohr's orbit in hydrogen and hydrogen-like substances can be computed by using the following formula.

radius of orbit=r=$\frac{n^2h^2}{4\pi^2m_ee^2} \times \frac1Z=0.529\times \frac{n^2}{Z}$ angstrom.


n=Principal quantum number, Z=Automic number, $m_e$=Electron mass, h=Plank's constant, e=Electron charge.

Now, the radius of Bohr's first orbit in $Li^{2+}$ =$r=\frac{4..39048e67J*Kg*m^2}{5.766618111e-48C*kg}=0.4746007565$m^2/F. Now, this value should be$=0.529\times\frac{1^2}{3}$ Angstrom. where 1 angstrom =100pm. So the R.H.S. of this equation 17.63 pm.

Now how to prove that L.H.S. of this equation = 17.63 pm using unit conversion calculator? What is F? How to write angstrom symbol here?
Apr 2015
The Angstom symbol, Å, is available from the Windows Character Map application Charmap.exe.

This is directly available from the Run box as charmap or charmap.exe.
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Jan 2020
Mumbai(Bombay), Maharashtra State, India.
How to convert $0.4756007565 m^2/F$ into 53 pm? I know $1F=\frac{C^2*s^2}{kg*m^2}$


Forum Staff
Jul 2013
Any place where Alyson Hannigan can find me
I'm not sure where you got your equation from?
\(\displaystyle r_n = \dfrac{4 \pi \epsilon _0 \hbar ^2}{m e^2} \dfrac{n^2}{Z}\)

(The \(\displaystyle \epsilon _0\) takes care of the problem that e is measured in C, so the unit F does not come up.)

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