Question

Which is the correct relationship :

• A. $E_{1}$ of $H=1 / 2\, E_{2}$ of $He ^{+}=1 / 3\, E _{3}$ of $Li ^{2+}=1 / 4\, E _{4}$ of $Be ^{3+}$
• B. $E _{1}( H )= E _{2}\left( He ^{+}\right)= E _{3}\left( Li ^{2+}\right)=$ $E _{4}\left( Be ^{3+}\right)$
• C. $E _{1}( H )=2 E _{2}\left( He ^{+}\right)=3 E _{3}\left( Li ^{2+}\right)=$ $4 E _{4}\left( Be ^{3+}\right)$
• D. No relation

Answer 1

Answer: (B)

$E _{1}( H )=-13.6 \times \frac{1^{2}}{1^{2}}=-13.6 \, eV ;$
$E _{2}\left( He ^{+}\right)=-13.6 \times \frac{2^{2}}{2^{2}}=-13.6\, eV$
$E _{3}\left( Li ^{2+}\right)=-13.6 \times \frac{3^{2}}{3^{2}}=-13.6 \, eV ;$
$E _{4}\left( Be ^{3+}\right)=-13.6 \times \frac{4^{2}}{4^{2}}=-13.6\, eV$
$\therefore E _{1}( H )= E _{2}\left( He ^{+}\right)$
$= E _{3}\left( Li ^{2+}\right)= E _{4}\left( Be ^{3+}\right)$