Excitation energy of a hydrogen like ion in its first excitation state is 40.8 eV. Energy needed to remove the electron from the ion in ground state is

Question

Excitation energy of a hydrogen like ion in its first excitation state is 40.8 eV. Energy needed to remove the electron from the ion in ground state is (A) 54.4 eV (B) 13.6 eV (C) 40.8 eV (D) 27.2 eV

Tardigrade Admin · Accepted Answer

Excitation energy Δ E=E2-E1=13.6Z2[(1/12)-(1/22)] 40.8=13.6Z2×(3/4) or Z = 2 So, energy required to remove the electron from ground state =+(13.6Z2/(1)2)=13.6(2)2 = 54.4 eV

Q. Excitation energy of a hydrogen like ion in its first excitation state is $40.8 e V$ . Energy needed to remove the electron from the ion in ground state is

$54.4 e V$

$13.6 e V$

$40.8 e V$

$27.2 e V$

Excitation energy
$Δ E = E_{2} - E_{1} = 13.6 Z^{2} [\frac{1}{1 ^{2}} - \frac{1}{2 ^{2}}]$
$40.8 = 13.6 Z^{2} \times \frac{3}{4}$
or $Z = 2$
So, energy required to remove the electron from ground state
$= + \frac{13.6 Z ^{2}}{( 1 ) ^{2}} = 13.6 (2)^{2}$
$= 54.4 e V$

Q. Excitation energy of a hydrogen like ion in its first excitation state is 40.8eV. Energy needed to remove the electron from the ion in ground state is

54.4eV

13.6eV

40.8eV

27.2eV