Statement I: Second orbit circumference of hydrogen atom is two times the de-Broglie wavelength of e

Question

Statement I: Second orbit circumference of hydrogen atom is two times the de-Broglie wavelength of electrons in that orbit.\ Statement II : de-Broglie wavelength of electron in ground state is minimum.

Professor PC Thomas Classes · Answer

(a) : $m v_2 r_2=2\left(\frac{h}{2 \pi}\right) \Rightarrow 2 \pi r_2=2\left(\frac{h}{m v_2}\right)=2 \lambda_2$ Further, $\lambda=\frac{h}{p}$ Speed of electron is maximum in ground state. Hence, $\lambda$ is minimum.