Question

If the velocity of an electron in the first Bohr orbit of a hydrogen atom is 2.187691 $\times$ 10${}^x$ m s${}^{-1}$, then value of $x$ is :

[Given: Radius of first Bohr's orbit= 0.529 $\mathring{A}$]

Answer 1

mvr = $\frac{nh}{2\pi }$

v = $\frac{nh}{2\pi mr}$

= $\frac{1\times 6.63\times {10}^{-34}}{2\times 3.14\times 9.1\times {10}^{-31}\times 0.529\times {10}^{-10}}=2.187691\times {10}^{6}m{s}^{-1}$

Hence, x is 6.