Which energy level of the singly ionized carb | vedclass

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(B) The energy of an electron in a hydrogen-like atom is given by the formula $E_n = -13.6 \frac{Z^2}{n^2} 	ext{ eV}$.For the hydrogen atom,the atomi

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$6$

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(B) The energy of an electron in a hydrogen-like atom is given by the formula $E_n = -13.6 \frac{Z^2}{n^2} 	ext{ eV}$.For the hydrogen atom,the atomic number $Z = 1$ and for the ground state,$n = 1$.Thus,the ground state energy of hydrogen is $E_H = -13.6 	imes \frac{1^2}{1^2} = -13.6 	ext{ eV}$.For a singly ionized carbon atom $(C^+)$,the atomic number $Z = 6$.We want to find the energy level $n$ such that the energy $E_C$ equals the ground state energy of hydrogen:$-13.6 \frac{6^2}{n^2} = -13.6$.Dividing both sides by $-13.6$,we get $\frac{36}{n^2} = 1$.Therefore,$n^2 = 36$,which gives $n = 6$.

Which energy level of the singly ionized carbon atom has the same energy as the ground state energy of the hydrogen atom?

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