Question

A positroniuim consists of an electron and a positron revolving about their common centre of mass. Calculate the kinetic energy of the electron in ground state:

• A. $1.51eV$
• B. $3.4eV$
• C. $6.8eV$
• D. $13.6eV$

Answer 1

The correct option is C $6.8eV$

$E_k\propto m$

Where $m$ is reduced mass of electron in the orbit.

For hydrogen atom $m=\frac{m_e{m}_p}{m_p+m_e}$ which is $m_e$ .......(1)

because mass of proton $m_p$ is much larger

than the mass of electron $m_e$.

Mass of positron is equal to mass of electron so reduced mass of electron

for this pair will be $m=m_e^2/2m_e=m_e/2$ ..............(2)

As energy for hydrogen atom is $13.6eV$

so energy for electron-positron pair will be $13.6/2=6.8eV$

Because in this case reduced mass is $m_e/2$ i.e. half of that in the case of hydrogen atom.(See equation-2 and equation-1)

Option C is correct.