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
Classically, an electron can be in any orbit around the nucleus of an atom. Then what determines the typical atomic size? Why is an atom not, say, a thousand times bigger than its typical size? The question had greatly puzzled Bohr before he arrived at his famous model of the atom that you have learnt in the text. To simulate what he might well have done before his discovery, let us play as follows with the basic constants of nature and see if we can get a quantity with the dimensions of length that is roughly equal to the known size of an atom (~ 10−10 m).
(a) Construct a quantity with the dimensions of length from the fundamental constants e, me, and c. Determine its numerical value.
(b) You will find that the length obtained in (a) is many orders of magnitude smaller than the atomic dimensions. Further, it involves c. But energies of atoms are mostly in non-relativistic domain where c is not expected to play any role. This is what may have suggested Bohr to discard c and look for ‘something else’ to get the right atomic size. Now, the Planck’s constant h had already made its appearance elsewhere. Bohr’s great insight lay in recognising that h, me, and e will yield the right atomic size. Construct a quantity with the dimension of length from h, me, and e and confirm that its numerical value has indeed the correct order of magnitude.
The first excited energy of a He+ ion is the same as the ground state energy of hydrogen. Is it always true that one of the energies of any hydrogen-like ion will be the same as the ground state energy of a hydrogen atom?
The minimum orbital angular momentum of the electron in a hydrogen atom is
In which of the following transitions will the wavelength be minimum?
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
Which of the following products in a hydrogen atom are independent of the principal quantum number n? The symbols have their usual meanings.
(a) vn
(b) Er
(c) En
(d) vr
Ionization energy of a hydrogen-like ion A is greater than that of another hydrogen-like ion B. Let r, u, E and L represent the radius of the orbit, speed of the electron, energy of the atom and orbital angular momentum of the electron respectively. In ground state
Find the radius and energy of a He+ ion in the states (a) n = 1, (b) n = 4 and (c) n = 10.
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.
Find the maximum Coulomb force that can act on the electron due to the nucleus in a hydrogen atom.
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?
Find the maximum angular speed of the electron of a hydrogen atom in a stationary orbit.
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).
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 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?
Electrons are emitted from an electron gun at almost zero velocity and are accelerated by an electric field E through a distance of 1.0 m. The electrons are now scattered by an atomic hydrogen sample in ground state. What should be the minimum value of E so that red light of wavelength 656.3 nm may be emitted by the hydrogen?
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.
