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  4. We consider the Thomson model of the hydrogen atom in which the proton charge is distributed uniformly over a spherical volume of radius 0.25 mathringA. Applying the Bohr condition in this model, the ground state energy (in eV) of the electron will be close to

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Q. We consider the Thomson model of the hydrogen atom in which the proton charge is distributed uniformly over a spherical volume of radius $0.25 \,\mathring{A}$. Applying the Bohr condition in this model, the ground state energy (in $eV$) of the electron will be close to

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Solution:

As per the condition given in question, we have following picture of atom,
image
As a spherical charge distribution acts like a point charge concentrated at centre, above model is equivalent to Bohr’s model.
Hence, we expert same energy value of electron as that of Bohr’s atom.
$\therefore $ Ground state energy of electron= $−136.\, eV$.
Note Question is incorrect as Thomson’s model does not have any ground state configuration.
Thomson’s model of $H$-atom is as shown below;
image
Now, if we calculate energy is above case, we get
$U=V_{\text{center}}=\frac{3}{2}\times\frac{1}{4\pi\varepsilon_{o}}\times\frac{e}{\varepsilon}\times-e$
$=-86.4\,eV$
Not matching with any option.