Question

According to Bohr model, the diameter of first orbit of hydrogen atom will be

• A. $1A^{\circ }$
• B. $0.529A^{\circ }$
• C. $2.25A^{\circ }$
• D. $0.725A^{\circ }$

Answer 1

The correct option is A $1A^{\circ }$

The radius of first orbit of hydrogen atom is:
$r=\frac{n^2{h}^2{ϵ}_0}{\pi m{e}^2}$ ........................(since, n = 1)

$r=\frac{\left(1{)}^2\right(6.6\times {10}^{-34}{)}^2(8.85\times {10}^{-12})}{\left(3.14\right)(9.1\times {10}^{-31})(1.6\times {10}^{-19}{)}^2}$

$r=0.529\times {10}^{-10}m$

$r=0.529A^{\circ }$

Therefore diameter of first orbit is:
$d=2r=2\left(0.529\right)=1.058$
$d\approx 1A^{\circ }$