It is similar in construction to an optical
spectrometer. It consists of three parts. (i) a source of X-rays (2) a crystal
held on a circular table which is graduated and provided with vernier and (3) a
detector (ionization chamber). X-rays from an X-ray tube, limited by two narrow
lead slits S1 and S2 are allowed to
fall upon the crystal C.
The crystal is mounted on the
circular table T, which can rotate about a vertical axis and its position can
be determined by the vernier V. The table is provided with a radial arm (R)
which carries an ionization chamber (I). This arm also can be rotated about the
same vertical axis as the crystal. The position of this arm can be determined
by a second vernier (not shown in the figure).
The
ionization chamber is connected to an electrometer (E) to measure the
ionization current.
Hence we can measure
the intensity of the diffracted beam of X-rays, diffracted in the direction of
the ionization chamber. S3 is a lead slit, to limit the width of the
diffracted beam. In practice, the crystal table is geared to the ionization
chamber so that the chamber turns through 2q when the crystal is turned through q.
Given : l = 0.3 Å, d = 0.5 Å
According to Bragg’s
law: -
2dsinq = nl Þ sinq = nl/2d ……..(i)
(i) For 2nd order Bragg’s
diffraction: -
In this case n = 2 then sinq = (2´0.3)/(2´0.5) = 0.6
Þ q = (36.869)0
(ii) For 3rd order Bragg’s
diffraction: -
In
this case n = 3 then sinq = (3 ´ 0.3)/(2 ´ 0.5) = 0.9
Þ q = (64.158)0
Q.4 A photon of frequency n is scattered by an electron initially at rest. Prove
that the maximum kinetic energy of the recoil electron is given by
(AKTU 2002-03, 2005-06)
Related
Questions -
Q. A photon of frequency m is scattered by
an electron initially at rest. Prove that the maximum kinetic energy of the
recoil electron is given
Ans: Kinetic Energy of The Recoil Electron: -
The K.E. of recoil electron is equal to the decrease
in the energy of the incident photon,
The energy of incident photon = hn, and energy of scattered photon = hn¢
The decrease in energy
of photon = hn - hn¢ = h(n - n¢) ……….(i)
Let m0c2 and mc2 be the rest
mass of energy and recoil energy of the electron respectively.
The kinetic energy of
recoil electron
= mc2 – m0c2 = (m – m0)c2 .………(ii)
This recoil energy is
equal to the decrease in energy of the incident photon.
So, K.E. of recoil
electron
Where Dl is the change in wavelength
