In the Auger process an atom makes a transition to a lower state … - Vidyadip

Question

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.

✓

Answer

As the nucleus is massive, 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 of the nth state $\text{En}=-\text{Z}^2\text{R}\frac{1}{\text{n}^2}$ where R is the Rydberg constant and Z = 24.
The energy released in a transition form 2 to 1 is $\Delta\text{t}=\text{Z}^2\text{R}\Big(1-\frac{1}{4}\Big)=\frac{3}{4}\text{Z}^2\text{R}$.
The energy required to eject a n = 4 electron is $\text{E}_4=\text{Z}^2\text{R}\frac{1}{16}$.
Thus, the kinetic energy of the Auger electron is $\text{KE}=\text{Z}^2\text{R}\Big(\frac{3}{4}-\frac{1}{16}\Big)=\frac{1}{16}\text{Z}^2\text{R}$
$=\frac{11}{16}\times24\times24\times13.6\text{eV}=5385.6\text{eV}.$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from Atoms→Atoms — all question types→Physics STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Plot a graph showing variation of voltage vs the current drawn from the cell. How can one get information from this plot about the emf of the cell and its internal resistance?
Two cells of emf’s $E_1$ and $E_2$ and internal resistance $r_1$ and $r_2$ are connected in parallel. Obtain the expression for the emf and internal resistance of a single equivalent cell that can replace this combination?

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 10eV when the electron is widely separated from the proton? Can we still write $\text{E}_\text{n}=\frac{\text{E}_1}{\text{n}^2}?\text{ r}_\text{n}=\text{a}_0\text{n}^2?$

Find the diameter of the image of the moon formed by a spherical concave mirror of focal length 7.6m. The diameter of the moon is 3450km and the distance between the earth and the moon is $3.8 \times 10^5km.$

A bar magnet of length 1cm and cross-sectional area $1.0cm^2$ produces a magnetic field of 1.5 × 10. T at a point in end-on position at a distance 15cm away from the centre.

Find the magnetic moment M of the magnet.
Find the magnetization I of the magnet.
Find the magnetic field B at the centre of the magnet.

In an imaginary atmosphere, the air exerts a small force $F$ on any particle in the direction of the particle's motion. A particle of mass $m$ projected upward takes a time $t_1$ in reaching the maximum height and $t_2$ in the return journey to the original point. Then:

Two particles A and B, having opposite charges $2.0 \times 10^{-6}$C and $2.0 \times 10^{-6}$C, are placed at a separation of 1.0cm.

Write down the electric dipole moment of this pair.
Calculate the electric field at a point on the axis of the dipole 1.0m awa.y from the centre.
Calculate the electric field at a point on the perpendicular bisector of the dipole and 1.0m away from the centre.

Suppose the space between the two inner shells of the previous problem is filled with a dielectric of dielectric coastant K. Find the capacitance of the system between A and B.

Two particles A and B of de Broglie wavelengths $\lambda _1$ and $\lambda _2$ combine to form a particle C. The process conserves momentum. Find the de Broglie wavelength of the particle C. (The motion is one dimensional).

A paperweight in the form of a hemisphere of radius 3.0cm is used to hold down a printed page. An observer looks at the page vertically through the paperweight. At what height above the page will the printed letters near the centre appear to the observer?

A solid sphere of mass m and radius r is placed inside a hollow thin spherical shell of mass M and radius R as shown in A particle of mass m' is placed on the line joining the two centres at a distance x from the point of contact of the sphere and the shell. Find the magnitude of the resultant gravitational force on this particle due to the sphere and the shell if,

r < x < 2r.
2r < x < 2R.
x > 2R.