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

#### WMDhamnekar

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.

Where,

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?

#### studiot

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.

topsquark

#### WMDhamnekar

How to convert $0.4756007565 m^2/F$ into 53 pm? I know $1F=\frac{C^2*s^2}{kg*m^2}$

#### topsquark

Forum Staff
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.)

-Dan

WMDhamnekar