Question

Imagine that the electron in a hydrogen atom is replaced by a muon $\left(\mu \right)$. The mass of a muon particle is $207times$ that of an electron and the charge is equal to the charge of an electron. The ionization potential of this hydrogen atom will be:

• A. $27.2eV$
• B. $331.2eV$
• C. $13.6eV$
• D. $2815.2eV$

Answer 1

The correct option is D

$2815.2eV$

Step 1: Given

Ratio of mass of muon to electron: $\frac{m_{\mu }}{m_e}=\frac{207}{1}$

Step 2: Formula Used

$E\propto m$

Step 3: Find the ionization potential

The ionization potential of the hydrogen atom is $E=13.6eV$. Since the mass is increased, the ionization potential will also increase in the same ratio as it is directly proportional to mass. Calculate the new ionization potential by multiplying the original ionization potential with the ratio of mass.

$$\begin{gathered} E\propto m \\ \Rightarrow E=13.6\times \frac{m_{\mu }}{m_e}eV \\ \Rightarrow E=13.6\times 207eV \\ \Rightarrow E=2815.2eV \end{gathered}$$

Hence, the ionization potential is $2815.2eV$.