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Question
Find the radius and energy of a He+ ion in the states (a) n = 1, (b) n = 4 and (c) n = 10.
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Solution
For He+ ion,
Atomic number, Z = 2
For hydrogen like ions, radius (r) of the nth state is given by
`r = (0.53 n^2)/ZÅ`
Here
Z= Atomic number of ions
n = Quantum number of the state
Energy (E) of the nth state is given by
`E_n = -(13.6 Z^2)/(n^2)`
(a)
for n = 1
Radius,
`r = (0.53xx(1)^2)/2`
`Å = 0.265 A^0`
Energy, En = `(-13.6 xx 4)/1`
= - 54.4 ev
(b)
For n = 4,
Radius, `r = (0.53xx16)/2 = 4.24 Å `
Energy, `E = (-13.6xx4)/16= -3.4 eV`
(c)
For n = 10,
`Radius, r = (0.53xx100)/2`
= 26.5 Å
Energy, E = `(-13.6 xx 4 )/100 = -0.544 eV`
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