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## Q. 1.1

Calculate the radii of the first, second and third permitted electron orbits in a Bohr’s hydrogen atom.

## Verified Solution

Radius of the nth orbit for hydrogen, $r_{n}=\frac{\varepsilon _{0}h^{2}n^{2} }{\pi mq^{2} }$

$=\frac{(8.854\times 10^{-12})(6.62\times 10^{-34} )^{2}n^{2} }{\pi (9.1\times 10^{-31} )(1.6\times 10^{-19} )^{2}}$

Therefore, the radius of the first orbit is,$r_{1}=5.27\times 10^{-11} \times 1^{2}m$

$=5.27\times 10^{-11}m=0.527A.U.$

The radius of the second orbit is,              $r_{2}=5.27\times 10^{-11} \times 2^{2}=2.108A.U.$

The radius of the third orbit is,                  $r_{3}=5.27\times 10^{-11} \times 3^{2}=4.743A.U.$