44: X-rays : Neet-xii-physics

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NEET-XII-Physics

44: X-rays

with Solutions - page 2

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Qstn #3
The energy of a photon of a characteristic X-ray from a Coolidge tube comes from
(a) the kinetic energy of the striking electron
(b) the kinetic energy of the free electrons of the target
(c) the kinetic energy of the ions of the target
(d) an atomic transition in the target
digAnsr: d
Ans : (d) an atomic transition in the target
In an X-ray tube, electrons are emitted by the filament. These electrons are made to strike the filament by applying an electric field between the filament and the target. As a result of it, the kinetic energy of the electrons is lost to the target atoms. This energy is utilised by the target atoms to knock out an electron from the innermost shell. Consequently, the electron makes a transition from the higher energy state to this vacant shell. Due to this transition, the difference of energy of the two states gives photon of characteristic X-ray.
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Qstn #4
If the potential difference applied to the tube is doubled and the separation between the filament and the target is also doubled, the cutoff wavelength
(a) will remain unchanged
(b) will be doubled
(c) will be halved
(d) will become four times the original
digAnsr: c
Ans : (c) will be halved
Cut off wavelength is given by
`` {\lambda }_{\,\mathrm{\,min\,}}=\frac{hc}{eV}``,
where h = Planck's constant
c = speed of light
e = charge on an electron
V = potential difference applied to the tube
When potential difference (V) applied to the tube is doubled, cutoff wavelength `` \left(\lambda {\text{'}}_{\,\mathrm{\,min\,}}\right)`` is given by
`` \lambda {\text{'}}_{\,\mathrm{\,min\,}}=\frac{hc}{e\left(2V\right)}``
`` \Rightarrow \lambda {\text{'}}_{\,\mathrm{\,min\,}}=\frac{{\lambda }_{min}}{2}``
Cuttoff wavelength does not depend on the separation between the filament and the target.
Thus, cutoff wavelength will be halved if the the potential difference applied to the tube is doubled.
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Qstn #5
If the current in the circuit for heating the filament is increased, the cutoff wavelength
(a) will increase
(b) will decrease
(c) will remain unchanged
(d) will change
digAnsr: c
Ans : (c) will remain unchanged
Cut off wavelength is given by
`` {\lambda }_{\,\mathrm{\,min\,}}=\frac{hc}{eV}``,
where h = Planck's constant
c = speed of light
e = charge on an electron
V = potential difference applied to the tube
Clearly, the cutoff wavelength does not depend on the current in the circuit and temperature of the filament.
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Qstn #6
Moseley’s Law for characteristic X-ray is √v = a(Z - b). Here,
(a) both a and b are independent of the material
(b) a is independent but b depends on the material
(c) b is independent but a depends on the material
(d) both a and b depend on the material
digAnsr: a
Ans : (a) both a and b are independent of the material
Moseley's Law for characteristic X-ray is √v = a(Z - b), where, a and b are constants independent of the material used.
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Qstn #7
Frequencies of Kα X-rays of different materials are measured. Which one of the graphs in the figure may represent the relation between the frequency v and the atomic number Z ?

Ans : Using Moseley's Law,
`` \sqrt{v}=a\left(Z-b\right)``,
where v = frequency of K_α X-ray
Z = atomic number
`` \therefore v={a}^{2}{\left(Z-b\right)}^{2}``
`` \Rightarrow {\left(Z-b\right)}^{2}=\frac{v}{{a}^{2}}``
This is the equation of a parabola with some intercept on the axis, representing atomic number (Z). Hence, curve d represent this relation correctly.
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Qstn #8
The X-ray beam emerging from an X-ray tube
(a) is monochromatic
(b) has all wavelengths smaller than a certain maximum wavelength
(c) has all wavelengths greater than a certain minimum wavelength
(d) has all wavelengths lying between a minimum and a maximum wavelength
digAnsr: c
Ans : (c) has all wavelengths greater than a certain minimum wavelength
The X-ray beam emerging from an X-ray tube consists of wavelengths greater than a certain minimum wavelength called cutoff wavelength.
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Qstn #9
One of the following wavelengths is absent and the rest are present in the X-rays coming from a Coolidge tube. Which one is the absent wavelength?
(a) 25 pm
(b) 50 pm
(c) 75 pm
(d) 100 pm
digAnsr: a
Ans : (a) 25 pm
Cutoff wavelength (minimum) is absent in the X-rays coming from a Coolidge tube. Hence, the 25 pm wavelength is absent.
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Qstn #10
The figure shows the intensity-wavelength relations of X-rays coming from two different Coolidge tubes. The solid curve represents the relation for the tube A in which the potential difference between the target and the filament is V_A and the atomic number of the target material is Z_A. These quantities are V_B and Z_B for the other tube. Then,
(a) V_A > V_B, Z_A > Z_B
(b) V_A > V_B, Z_A < Z_B
(c) V_A < V_B, Z_A > Z_B
(d) V_A > V_B, Z_A < Z_B
Figure
digAnsr: b
Ans : (b) V_A > V_B, Z_A < Z_B
It is clear from the figure that the X-ray of tube A has less cutoff wavelength than the X-ray of tube B.
`` \therefore {\lambda }_{A}<{\lambda }_{B}``
Using Moseley's Law,
`` {Z}_{A}<{Z}_{B}``
`` \lambda \propto \frac{1}{V}``, where V is the voltage applied in the X-ray tube.
`` \therefore {V}_{A}>{V}_{B}``
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Qstn #11
50% of the X-rays coming from a Coolidge tube are able to pass through a 0.1 mm thick aluminium foil. If the potential difference between the target and the filament is increased, the fraction of the X-rays passing through the same foil will be
(a) 0%
(b) < 50%
(c) 50 %
(d) > 50%
digAnsr: d
Ans : (d) > 50%
The penetrating power of X-rays varies directly with the accelerating potential of the electrons (V) or the energy of the X-rays. So, if the potential difference between the target and the filament is increased, the fraction of the X-rays passing through the foil will also increase.
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Qstn #12
50% of the X-ray coming from a Coolidge tube is able to pass through a 0.1 mm thick aluminium foil. The potential difference between the target and the filament is increased. The thickness of the aluminium foil that will allow 50% of the X-ray to pass through will be
(a) zero
(b) < 0.1 mm
(c) 0.1 mm
d) > 0.1 mm
digAnsr: d
Ans : (d) > 0.1 mm
As we increase the accelerating potential between the filament and the target, the penetrating power of the X-ray will increase. As a result, the fraction of the X-ray passing through the foil will increase. But it is given that the same fraction of the X-ray is passing. Therefore, the thickness of the aluminium foil should be increased to maintain the same fraction of the X-ray that will pass through the foil.
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Qstn #13
X-ray from a Coolidge tube is incident on a thin aluminium foil. The intensity of the X-ray transmitted by the foil is found to be I₀. The heating current is increased to increase the temperature of the filament. The intensity of the X-ray transmitted by the foil will be
(a) zero
(b) < I₀
(c) I₀
(d) > I₀
digAnsr: d
Ans : (d) > I₀_.
We know that the intensity of an X-ray is directly proportional to the current through the X-ray tube. If the filament current is increased to increase the temperature of the filament, more electrons will be emitted from the filament per unit time. As a result, current in the X-ray tube will increase and consequently, the intensity of the X-ray will also increase.
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Qstn #14
Visible light passing through a circular hole forms a diffraction disc of radius 0.1 mm on a screen. If an X-ray is passed through the same setup, the radius of the diffraction disc will be
(a) zero
(b) < 0.1 mm
(c) 0.1 mm
(d) > 0.1 m
digAnsr: b
Ans : (b) < 0.1 mm
Radius of the diffraction disc is directly proportional to the wavelength of the light used for the given hole. We know that the wavelength of an X-ray is less than the wavelength of visible light. If an X-ray is passed through the same setup, the radius of the diffraction disc will be less than 0.1 m.
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#
Section : iii

Qstn #1
For harder X-rays,
(a) the wavelength is higher
(b) the intensity is higher
(c) the frequency is higher
(d) the photon energy is higher.
digAnsr: c,d
Ans : (c) the frequency is higher
(d) the photon energy is higher
Harder X-rays are the X-rays having low wavelengths. Since the frequency varies inversely with the wavelength, hard X-rays have high frequency.
Energy of a photon `` \left(E\right)`` is given by
`` E=\frac{hc}{\lambda }``
Here,
h = Planck's constant
c = Speed of light
`` \lambda `` = Wavelength of light.
Clearly, energy varies inversely with wavelength. Therefore, the energy of the photon will be higher for the hard X-ray.
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Qstn #2
Cutoff wavelength of X-rays coming from a Coolidge tube depends on the
(a) target material
(b) accelerating voltage
(c) separation between the target and the filament
(d) temperature of the filament.
digAnsr: b
Ans : (b) accelerating voltage
Cutoff wavelength `` \left({\lambda }_{\,\mathrm{\,min\,}}\right)`` is given by
`` {\lambda }_{\,\mathrm{\,min\,}}=\frac{hc}{eV}``
Here,
h = Planck's constant
c = Speed of light
V = Accelerating voltage
e = Charge of electron
Clearly, a cutoff wavelength depends on accelerating voltage. It does not depend on the target material, separation between the target and the temperature of the filament.
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