If the atom _{100}Fm^{257} follows the Bohr m | vedclass

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(D) The radius of an orbit in the Bohr model is given by $r_n = n^2 \frac{a_0}{Z}$,where $a_0$ is the Bohr radius $(0.529 \ \mathring{A})$,$n$ is the

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$0.25$

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(D) The radius of an orbit in the Bohr model is given by $r_n = n^2 \frac{a_0}{Z}$,where $a_0$ is the Bohr radius $(0.529 \ \mathring{A})$,$n$ is the principal quantum number,and $Z$ is the atomic number.Given the atom is $_{100}Fm^{257}$,the atomic number $Z = 100$.The outermost shell for Fermium $(Z=100)$ is the $5f$ shell,so the principal quantum number $n_{shell} = 5$.The radius of the outermost shell is $r = (5)^2 \frac{a_0}{100} = \frac{25}{100} a_0 = 0.25 a_0$.Thus,the radius is $0.25$ times the Bohr radius,so $n = 0.25$.

If the atom $_{100}Fm^{257}$ follows the Bohr model and the radius of the outermost shell of $_{100}Fm^{257}$ is $n$ times the Bohr radius,then find $n$.

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