If the radius of the first orbit of a hydroge | vedclass

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(B) The radius of a hydrogen-like ion is given by $r = \frac{0.0529 	imes n^2}{Z} \ nm$.Given $r = 1.763 	imes 10^{-2} \ nm$ and $n = 1$.Substitutin

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$-1.962 	imes 10^{-17}$

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(B) The radius of a hydrogen-like ion is given by $r = \frac{0.0529 	imes n^2}{Z} \ nm$.Given $r = 1.763 	imes 10^{-2} \ nm$ and $n = 1$.Substituting the values: $1.763 	imes 10^{-2} = \frac{0.0529 	imes (1)^2}{Z}$.$Z = \frac{0.0529}{0.01763} \approx 3$.The energy of an orbit is given by $E = -2.18 	imes 10^{-18} 	imes \frac{Z^2}{n^2} \ J$.Substituting $Z = 3$ and $n = 1$: $E = -2.18 	imes 10^{-18} 	imes \frac{3^2}{1^2} \ J$.$E = -2.18 	imes 10^{-18} 	imes 9 \ J = -19.62 	imes 10^{-18} \ J$.$E = -1.962 	imes 10^{-17} \ J$.

If the radius of the first orbit of a hydrogen-like ion is $1.763 \times 10^{-2} \ nm$, the energy associated with that orbit (in $J$) is

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