the ratio between total acceleration of the electron in singly ionized helium atom and doubly ionized lithium atom is
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According Bohr's model of an atom V_n=2.18\times 10^\dfrac{z}{n}\propto \dfrac{z}{n}V
n
=2.18×10
n
z
∝
n
z
r_n=0.529\dfrac{n^2}{z}\propto \dfrac{n^2}{z}r
n
=0.529
z
n
2
∝
z
n
2
The angular acceleration of the electron a=\dfrac{v^2_n}{r_n}\propto\dfrac{z^3}{n^4}a=
r
n
v
n
2
∝
n
4
z
3
for ground state n=1n=1
\Rightarrow a\propto z^3⇒a∝z
3
\dfrac{a_{He}}{a_{Li}}=\dfrac{z^3_{He}}{z^3_{Li}}=\dfrac{z^3}{3^3}=\dfrac{8}{27}
a
Li
a
He
=
z
Li
3
z
He
3
=
3
3
z
3
=
27
8
z_{He}=2z
He
=2
z_{Li}=3z
Li
=3.
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