A single electron ion has charge+Ze where Z is atomic number and e is electronic charge it requires 16 - Chemistry - Atomic Structure

Question

A single electron ion has charge+Ze where Z is atomic number and
e is electronic charge it requires 16 52eV to excite the electron
from the second Bohr orbit to third Bohr orbit find
- Atomic number of element
- The energy required for transition of electron from first to
third orbit
- Wavelength of photon required to remove electron from first
Bohr orbit to infinity
- The Kinetic Energy of electron in first Bohr orbit

Vartika Jain · Accepted Answer

Dear Student,

(a) 1 eV = 1
602×10-12 ergAlso, ∆E=hcλ=E3-E2                = RH
c h Z2[122-132]or, 16 52×1
602×10-12=109678 Z2 [122-132]×3×1010×6
626×10-27Z2=16 52×1
602×10-12109678×3×1010×6
626×10-27×365Z2=8
7400 or, Z≈3(b) ∆E=E3-E1 = RH
c h
Z2[112-132]                              = 109678×3×1010×6
626×10-27×32×89                              =17
4×10-11 erg(c) 1λ=RH
Z2[112-1∞2]1λ=109678×9or, λ=1
01×10-6 cm(d) K E
=12mv2              =12m(2πZe2nh) =2π2Z2e4mn2h2              =2×(3
14)2×32×(4 803×10-10)4×9
108×10-2812×(6
625×10-27)2              = 2
17×10-11 erg