The radius of an electron in the ground state | vedclass

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(D) The radius of an electron in the $n^{th}$ orbit of a hydrogen-like atom is given by the formula $r_n = r_1 \cdot n^2$,where $r_1$ is the radius of

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$106$

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(D) The radius of an electron in the $n^{th}$ orbit of a hydrogen-like atom is given by the formula $r_n = r_1 \cdot n^2$,where $r_1$ is the radius of the first orbit (ground state).Given: $r_1 = 1.06 \, \mathring{A}$ and $n = 10$.Substituting the values into the formula:$r_{10} = 1.06 	imes (10)^2$$r_{10} = 1.06 	imes 100$$r_{10} = 106 \, \mathring{A}$.Therefore,the radius of the electron in the $10^{th}$ orbit is $106 \, \mathring{A}$.

The radius of an electron in the ground state of hydrogen is $1.06 \, \mathring{A}$. What will be the radius of the electron in the $10^{th}$ orbit in $\mathring{A}$?

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