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

Radius of the first orbit of the electron in a hydrogen atom is $0.53 \; \mathring{A}$. So,the radius of the third orbit will be ........... $\mathring{A}$.

If the energy of a hydrogen atom in the $n^{th}$ orbit is ${E_n}$,then the energy in the $n^{th}$ orbit of a singly ionized helium atom will be:

Assuming the atom is in the ground state, the expression for the magnetic field at the nucleus in a hydrogen atom due to the circular motion of the electron is [$\mu_0 =$ permeability of free space, $m =$ mass of electron, $\epsilon_0 =$ permittivity of free space, $h =$ Planck's constant].

The following parameter is the same for all hydrogen-like atoms and ions in their ground state.

In the hydrogen atom, the radii of the first four Bohr orbits are related as:

Vedclass Test Series

Exam Paper Generator

Online Exam Module