The radius of the second Bohr orbit for hydrogen atom is (planck’s constant (h) = 6.6262×10−34Js mass of electron = 9.1091×10−31Kgcharge of electron ; (e)=1.6021×10−19Cpermittivity of vacum (∈0)=8.854185×10−12Kg−1m3A2

# The radius of the second Bohr orbit for hydrogen atom is (planck’s constant (h) = $6.6262×{10}^{-34}Js$ mass of electron = $9.1091×{10}^{-31}Kg$charge of electron ; $\left(e\right)=1.6021×{10}^{-19}C$permittivity of vacum $\left({\in }_{0}\right)=8.854185×{10}^{-12}K{g}^{-1}{m}^{3}{A}^{2}$

1. A

$1.65Å$

2. B

$4.76Å$

3. C

$0.529Å$

4. D

$2.12Å$

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### Solution:

Bohr radius  $\left({r}_{n}\right)$  $={\in }_{0}{n}^{2}{h}^{2}$

${r}_{n}=\frac{{n}^{2}{h}^{2}}{4{\pi }^{2}m{e}^{2}kZ}$

$k=\frac{1}{4\pi {\in }_{0}}$

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Where, m = mass of electron

e = charge of electron

h = Planck’s constant

k = Coulomb constant

${r}_{n}=\frac{{n}^{2}×0.53}{Z}Å$

Radius of  nth  Bohr orbit for H – atom = 0.53 ${n}^{2}Å$

$\therefore$Radius of 2nd Bohr orbit for H – atom

$=0.53×{\left(2\right)}^{2}=2.12Å$

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