Qstnid -Iv-6-find The Radius And Energy Of A He<sup>+</sup> Ion In The States (A) N = 1, (B) N = 4 And (C) N = 10. - 43: Bohr's Model And Physics Of The Atom - Neet-xii-physics

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NEET-XII-Physics

43: Bohr's Model and Physics of the Atom

with Solutions - page 4

Qstn# iv-6 Prvs-Qstn Next-Qstn

#6
Find the radius and energy of a He⁺ ion in the states (a) n = 1, (b) n = 4 and (c) n = 10.
Ans : For He⁺ ion,
Atomic number, Z = 2
For hydrogen like ions, radius `` \left(r\right)`` of the nth state is given by
`` r=\frac{0.53{n}^{2}}{Z}``Å
Here,
Z = Atomic number of ions
n = Quantum number of the state
Energy `` \left(E\right)`` of the nth state is given by
E_n = `` -\frac{13.6{Z}^{2}}{{n}^{2}}`` (a) For n = 1,
Radius, `` r=\frac{0.53\times {\left(1\right)}^{2}}{2}``
`` =0.265{\,\mathrm{\,A\,}}^{0}`` Å
Energy, E_n = `` \frac{-13.6\times 4}{1}``
= `` -`` 54.4 eV (b) For n = 4,
Radius, `` r=\frac{0.53\times 16}{2}=4.24\,\mathrm{\,\AA \,}``
Energy, `` E=\frac{-13.6\times 4}{16}=-3.4e\,\mathrm{\,V\,}`` (c) For n = 10,
Radius, `` r=\frac{0.53\times 100}{2}``
= 26.5 Å
Energy, `` E=\frac{-13.6\times 4}{100}=-0.544\,\mathrm{\,eV\,}``
Page No 384:

#6-a
n = 1,
Ans : For n = 1,
Radius, `` r=\frac{0.53\times {\left(1\right)}^{2}}{2}``
`` =0.265{\,\mathrm{\,A\,}}^{0}`` Å
Energy, E_n = `` \frac{-13.6\times 4}{1}``
= `` -`` 54.4 eV

#6-b
n = 4 and
Ans : For n = 4,
Radius, `` r=\frac{0.53\times 16}{2}=4.24\,\mathrm{\,\AA \,}``
Energy, `` E=\frac{-13.6\times 4}{16}=-3.4e\,\mathrm{\,V\,}``

#6-c
n = 10.
Ans : For n = 10,
Radius, `` r=\frac{0.53\times 100}{2}``
= 26.5 Å
Energy, `` E=\frac{-13.6\times 4}{100}=-0.544\,\mathrm{\,eV\,}``
Page No 384: