Energy of an electron in the second orbit of hydrogen atom is E 2 . The energy of electron in the third orbit of He +will be

Question

Energy of an electron in the second orbit of hydrogen atom is E 2 . The energy of electron in the third orbit of He +will be (A) (9/16) E 2 (B) (16/9) E 2 (C) (3/16) E 2 (D) (16/3) E 2

Tardigrade Admin · Accepted Answer

For 2 text nd orbit of H-atom E 2=(-13 ⋅ 6/22) eV For 3 text rd orbit of He + E 3 He + =(-13 ⋅ 6/32) 22 =(-13 ⋅ 6/4) × (4/9) × 22 = E 2 × (16/9)=(16/9) E 2

Q. Energy of an electron in the second orbit of hydrogen atom is $E_{2} .$ The energy of electron in the third orbit of $H e^{+}$ will be

$\frac{9}{16} E_{2}$

$\frac{16}{9} E_{2}$

$\frac{3}{16} E_{2}$

$\frac{16}{3} E_{2}$

For $2^{nd}$ orbit of H-atom
$E_{2} = \frac{- 13 \cdot 6}{2 ^{2}} e V$
For $3^{rd}$ orbit of $H e^{+}$
$E_{3}^{H e^{+}} = \frac{- 13 \cdot 6}{3 ^{2}} 2^{2}$
$= \frac{- 13 \cdot 6}{4} \times \frac{4}{9} \times 2^{2}$
$= E_{2} \times \frac{16}{9} = \frac{16}{9} E_{2}$

Q. Energy of an electron in the second orbit of hydrogen atom is E2​. The energy of electron in the third orbit of He+will be

169​E2​

916​E2​

163​E2​

316​E2​