Question

Question 2.34 Calculate the energy required for the process

He+ (g) ----> He 2+(g) + e-

The ionization energy for the H atom in the ground state is 2.18 ×10–18 J atom–1

Class XI Structure of Atom Page 67

Answer 1

The energy required for the process is 8.72×10^-18J.

Answer 2

According to Bohr's theory , we know,
energy of electron in unielectron atomic system ,
En = -2π²mZ²e⁴/n²h²

For H - atom,
ionisation energy is the energy required to remove a electron from ground state to infinity .
$e.g.,I.E=E_{\infty}-E_1$

I.E = 0 - ( - 2π²m1²e⁴/1²h² ) [ because n = 1, Z = 1]
= 2π²me⁴/h²
after putting π = 3.14
m = 9.1 × 10^-31 Kg
e = 1.602 × 10^-19 C
h = 6.626 × 10^-34 Js

then ,we get I.E = 2.18 × 10^-18 J/atom

now, for He^+ atom ,
IE = 0 - { -2πm(2)²e⁴/1²h²} [ because n = 1, Z = 2]
I.E = 4 × { 2π²me⁴/h²} = 4 × 2.18 × 10^-18 J/atom
= 8.72 × 10^-18 J/atom

hence, the energy required for the given process is 8.72 × 10^-18 J/atom