An electron in the ground state of the hydrogen atom has the orbital radius of $5.3 imes10^{-11}$ m while that for the electron in third excited state is $8.48 imes10^{-10}$ m. The ratio of the de Broglie wavelengths of electron in the excited state to that in the ground state is

Question

An electron in the ground state of the hydrogen atom has the orbital radius of $5.3	imes10^{-11}$ m while that for the electron in third excited state is $8.48	imes10^{-10}$ m. The ratio of the de Broglie wavelengths of electron in the excited state to that in the ground state is

Dr. Abubacker · Accepted Answer

[Solution by Dr. Abubacker] $\lambda=\frac{2\pi r}{n}$. The third excited state has $n=4$ and $r_4=16r_1$, so $\frac{\lambda_4}{\lambda_1}=\frac{16/4}{1}=4$. Answer (4).

Q. An electron in the ground state of the hydrogen atom has the orbital radius of $5.3\times10^{-11}$ m while that for the electron in third excited state is $8.48\times10^{-10}$ m. The ratio of the de Broglie wavelengths of electron in the excited state to that in the ground state is

Explanation

Reviewed by Dr. Abubacker

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