Question

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

• A. $-13.6/4$
• B. $-13.6$
• C. $-13.6/2$
• D. $-2\times 13.6$

Answer 1

Answer: (B)

As per the condition given in question, we have following picture of atom,

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;

Now, if we calculate energy is above case, we get
$U=V_{\text{center}}=\frac{3}{2}\times \frac{1}{4\pi {\epsilon }_o}\times \frac{e}{\epsilon }\times -e$
$=-86.4eV$
Not matching with any option.