Advertisements
Advertisements
प्रश्न
Positronium is just like a H-atom with the proton replaced by the positively charged anti-particle of the electron (called the positron which is as massive as the electron). What would be the ground state energy of positronium?
उत्तर
Positronium (Ps) is a system consisting of an electron and its anti-particle a positron, bound together into an exotic atom, specifically anonium. The system is unstable: the two particles annihilate each other to predominantly produce two or three gamma-rays, depending on the relative spin states. The orbit and energy levels of the two particles arc similar to that of the hydrogen atom (which is a bound slate of a proton and an electron). However, because of the reduced mass, the frequencies of the spectral lines are less than half of the corresponding hydrogen lines.
As in the new H-atom (positronium), the proton is replaced by the position of mass m = me/2 as under
Mass of positronium = m = `m_e^- + m_e^+`
`m_e^+ = m_e^(-1) = m_e/2`
As En = – 13.6 and so the energy of positron
`E_n = (-m_e^+e^4)/(8ε_0n^2h^2) = (-[m_e/2]e^4)/(8ε_0n^2h^2) = (-13.6)/2`
So `E_n = 13.6/2` ......`(∵ m_e = m/2)`
En = – 6.8 eV
APPEARS IN
संबंधित प्रश्न
Which wavelengths will be emitted by a sample of atomic hydrogen gas (in ground state) if electrons of energy 12.2 eV collide with the atoms of the gas?
The minimum orbital angular momentum of the electron in a hydrogen atom is
An electron with kinetic energy 5 eV is incident on a hydrogen atom in its ground state. The collision
A hydrogen atom emits ultraviolet radiation of wavelength 102.5 nm. What are the quantum numbers of the states involved in the transition?
A group of hydrogen atoms are prepared in n = 4 states. List the wavelength that are emitted as the atoms make transitions and return to n = 2 states.
What is the energy of a hydrogen atom in the first excited state if the potential energy is taken to be zero in the ground state?
Suppose, in certain conditions only those transitions are allowed to hydrogen atoms in which the principal quantum number n changes by 2. (a) Find the smallest wavelength emitted by hydrogen. (b) List the wavelength emitted by hydrogen in the visible range (380 nm to 780 nm).
A hydrogen atom in ground state absorbs a photon of ultraviolet radiation of wavelength 50 nm. Assuming that the entire photon energy is taken up by the electron with what kinetic energy will the electron be ejected?
Consider an excited hydrogen atom in state n moving with a velocity υ(ν<<c). It emits a photon in the direction of its motion and changes its state to a lower state m. Apply momentum and energy conservation principles to calculate the frequency ν of the emitted radiation. Compare this with the frequency ν0 emitted if the atom were at rest.
Let En = `(-1)/(8ε_0^2) (me^4)/(n^2h^2)` be the energy of the nth level of H-atom. If all the H-atoms are in the ground state and radiation of frequency (E2 - E1)/h falls on it ______.
- it will not be absorbed at all.
- some of atoms will move to the first excited state.
- all atoms will be excited to the n = 2 state.
- no atoms will make a transition to the n = 3 state.
