Positronium is just like a H-atom with the pr | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Positronium is a binary system consisting of an electron and a positron. Both particles revolve around their common center of mass.To treat this a

Vedclass · Accepted Answer

-$6.8$ eV

Vedclass · Answer

(B) Positronium is a binary system consisting of an electron and a positron. Both particles revolve around their common center of mass.To treat this as a single-particle system,we use the reduced mass $\mu$ of the binary system:$\mu = \frac{m_1 m_2}{m_1 + m_2} = \frac{m_e 	imes m_e}{m_e + m_e} = \frac{m_e}{2} = \frac{m}{2}$The ground state energy of an electron in a hydrogen atom is given by:$E_1 = -\frac{m e^4}{8 \epsilon_0^2 h^2} = -13.6 	ext{ eV}$Since the energy of the ground state is directly proportional to the mass of the orbiting particle,the ground state energy of positronium $E_1'$ is:$E_1' = \frac{\mu}{m} E_1 = \frac{m/2}{m} E_1 = \frac{1}{2} E_1$Substituting the value of $E_1$:$E_1' = \frac{1}{2} (-13.6 	ext{ eV}) = -6.8 	ext{ eV}$

Positronium is just like a $H$-atom with the proton replaced by the positively charged antiparticle of the electron (called the positron,which is as massive as the electron). What would be the ground state energy of positronium?

Similar Questions

Explain the limitations of the Bohr atomic model.

The de-Broglie wavelength associated with an electron of a hydrogen atom in its ground state is (in $\text{ Å}$)

According to Bohr's atomic model,which of the following is $NOT$ a possible energy for a photon emitted by a hydrogen atom (in $;eV$)? (in $eV$)

An electron in the hydrogen atom excites from the $2^{nd}$ orbit to the $4^{th}$ orbit. The change in angular momentum of the electron is (Planck's constant $h = 6.64 \times 10^{-34} \ J \cdot s$).

What is the ratio of the time periods of an electron in the $n = 2$ and $n = 1$ orbits of a hydrogen atom (in $:1$)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module