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(B) The radius of the $n^{th}$ Bohr orbit is given by the formula $r_n = a_0 n^2$,where $a_0$ is the Bohr radius and $n$ is the principal quantum numb

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$L$ and $K$

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(B) The radius of the $n^{th}$ Bohr orbit is given by the formula $r_n = a_0 n^2$,where $a_0$ is the Bohr radius and $n$ is the principal quantum number. Given the ratio of the radii $r_1 : r_2 = 4 : 1$,we have $\frac{n_1^2}{n_2^2} = \frac{4}{1}$,which implies $\frac{n_1}{n_2} = \frac{2}{1}$. Thus,$n_1 = 2$ and $n_2 = 1$. The orbit with $n=1$ is designated as $K$ and the orbit with $n=2$ is designated as $L$. Therefore,the designations are $L$ and $K$.

The ratio of the radii of two Bohr orbits of a hydrogen atom is $4:1$. What are their designations?

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