Advertisements
Advertisements
प्रश्न
In the Auger process an atom makes a transition to a lower state without emitting a photon. The excess energy is transferred to an outer electron which may be ejected by the atom. (This is called an Auger electron). Assuming the nucleus to be massive, calculate the kinetic energy of an n = 4 Auger electron emitted by Chromium by absorbing the energy from a n = 2 to n = 1 transition.
Advertisements
उत्तर
Auger Effect: The Auger effect is a process by which electrons with characteristic energies are ejected from atoms in response to a downward transition by another electron in the atom. In Auger spectroscopy, the vacancy is produced by bombardment with high-energy electrons, but the Auger effect can occur if the vacancy is produced by other interactions. It is observed as one of the methods of electron rearrangement after electron capture into the nucleus.
If an inner shell electron is removed from an atom, an electron from a higher level will quickly make the transition downward to fill the vacancy. Sometimes this transition will be accompanied by an emitted photon whose quantum energy matches the energy gap between the upper and lower level. Since for heavy atoms this quantum energy will be in the x-ray region, it is commonly called x.-ray fluorescence. This emission process for lighter atoms and outer electrons gives rise to line spectra.
In other cases, the energy released by the downward transition is given to one of the outer electrons instead of to a photon, and this electron is then ejected from the atom with an energy equal to. the energy lost by the electron which made the downward transition minus the binding energy of the electron that is ejected from the atom. Though more involved in interpretation than optical spectra, the analysis of the energy spectrum of these emitted electrons does give information about dying atomic energy levels. The Auger effect bears some resemblance to the internal conversion of the nucleus, which also ejects an electron.
Sometimes an upper election drops to fill the vacancy, emitting a photon.
As the nucleus is massive, the recoil momentum of the atom may be neglected and the entire energy of the transition may be considered transferred to the Auger electron. As there is a single valence electron in Cr, the energy states may be thought of as given by the Bohr model.
The energy En of the nth state
`E_n = + Z^2 R[1/n_1^2 - 1/n_2^2]`
= `Z^2 R [1/1 - 1/4]` .....[For n1 = 1, n2 = 2]
Z = 24
R = Rydberg constant
∴ `E_n = 3/4 Z^2 R`
The energy required to eject an electron from n = 4 state is `E_4 = Z^2 R 1/4^2 = 1/16 Z^2 R`
The energy given to electron is converted into KE. of the ejected electron.
Hence, the KE. of Auger (ejected) electron = En – E4
K.E. = `Z^2R 3/4 - 1/16 Z^2R`
= `11/16 Z^2R`
= `11/16 xx 24 xx 24 xx 13.6` eV
K.E. = 11 × 36 × 13.6 = 5385.6 eV
APPEARS IN
संबंधित प्रश्न
If Bohr’s quantisation postulate (angular momentum = nh/2π) is a basic law of nature, it should be equally valid for the case of planetary motion also. Why then do we never speak of quantisation of orbits of planets around the sun?
Find the wavelength of the electron orbiting in the first excited state in hydrogen atom.
When white radiation is passed through a sample of hydrogen gas at room temperature, absorption lines are observed in Lyman series only. Explain.
What will be the energy corresponding to the first excited state of a hydrogen atom if the potential energy of the atom is taken to be 10 eV when the electron is widely separated from the proton? Can we still write En = E1/n2, or rn = a0 n2?
Which of the following curves may represent the speed of the electron in a hydrogen atom as a function of trincipal quantum number n?
A hydrogen atom in ground state absorbs 10.2 eV of energy. The orbital angular momentum of the electron is increased by
A hydrogen atom emits ultraviolet radiation of wavelength 102.5 nm. What are the quantum numbers of the states involved in the transition?
(a) Find the first excitation potential of He+ ion. (b) Find the ionization potential of Li++ion.
A hydrogen atom in a state having a binding energy of 0.85 eV makes transition to a state with excitation energy 10.2 e.V (a) Identify the quantum numbers n of the upper and the lower energy states involved in the transition. (b) Find the wavelength of the emitted radiation.
A hydrogen atom in state n = 6 makes two successive transitions and reaches the ground state. In the first transition a photon of 1.13 eV is emitted. (a) Find the energy of the photon emitted in the second transition (b) What is the value of n in the intermediate state?
A gas of hydrogen-like ions is prepared in a particular excited state A. It emits photons having wavelength equal to the wavelength of the first line of the Lyman series together with photons of five other wavelengths. Identify the gas and find the principal quantum number of the state A.
Find the temperature at which the average thermal kinetic energy is equal to the energy needed to take a hydrogen atom from its ground state to n = 3 state. Hydrogen can now emit red light of wavelength 653.1 nm. Because of Maxwellian distribution of speeds, a hydrogen sample emits red light at temperatures much lower than that obtained from this problem. Assume that hydrogen molecules dissociate into atoms.
Show that the ratio of the magnetic dipole moment to the angular momentum (l = mvr) is a universal constant for hydrogen-like atoms and ions. Find its value.
A hydrogen atom moving at speed υ collides with another hydrogen atom kept at rest. Find the minimum value of υ for which one of the atoms may get ionized.
The mass of a hydrogen atom = 1.67 × 10−27 kg.
When a photon is emitted from an atom, the atom recoils. The kinetic energy of recoil and the energy of the photon come from the difference in energies between the states involved in the transition. Suppose, a hydrogen atom changes its state from n = 3 to n = 2. Calculate the fractional change in the wavelength of light emitted, due to the recoil.
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.
In a hydrogen atom the electron moves in an orbit of radius 0.5 A° making 10 revolutions per second, the magnetic moment associated with the orbital motion of the electron will be ______.
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.
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?
