NEET-XII-Physics
43: Bohr's Model and Physics of the Atom
- #9The energy of an atom (or ion) in its ground state is -54.4 eV. It may be
(a) hydrogen
(b) deuterium
(c) He+
(d) Li++digAnsr: cAns : (c) He+
The total energy of a hydrogen-like ion, having Z protons in its nucleus, is given by
`` E=-\frac{13.6{Z}^{2}}{{n}^{2}}`` eV
Here, n = Principal quantum number
For ground state,
n = 1
∴ Total energy, E = `` -`` 13.6 Z2 eV
For hydrogen,
Z = 1
∴ Total energy, E = `` -`` 13.6 eV
For deuterium,
Z = 1
∴ Total energy, E = `` -`` 13.6 eV
For He+,
Z = 2
∴ Total energy, E = `` -`` 13.6×22 = `` -`` 54.4 eV
For Li++,
Z = 3
∴ Total energy, E = `` -`` 13.6×32 = `` -`` 122.4 eV
Hence, the ion having an energy of -54.4 eV in its ground state may be He+.
Page No 383: