Question

The magnitude of angular momentum, orbit radius and frequency of revolution of electron in hydrogen atom corresponding to quantum number n are L, r and f respectively. Then according to Bohr's theory of hydrogen atom,

• A. \(fr^2L\) is constant for all orbits
• B. frL is constant for all orbits
• C. \(f^2rL\) is constant for all orbits
• D. \(frL^2\) is constant for all orbits

Answer 1

The correct option is B frL is constant for all orbits

$\frac{m{v}^2}{r}=\frac{k{q}^2}{r^2}\Rightarrow m{v}^{2}r=k{q}^2\left(mvr\right)v=k{q}^{2}lv=k{q}^2\cdots \left(1\right)Also,v=\frac{2\pi r}{T}=2\pi f\cdots \left(2\right)\left(2\right)in\left(1\right)gives,L\left(2\pi rf\right)=k{q}^2\Rightarrow frL=constant\left(B\right)$