HC Verma solutions for Concepts of Physics Vol. 2 [English] Class 11 and 12 chapter 22 - X-rays [Latest edition]

In a Coolidge tube, electrons strike the target and stop inside it. Does the target get more and more negatively charged as time passes?

Can X-rays be polarised?

X-ray and visible light travel at the same speed in vacuum. Do they travel at the same speed in glass?

Characteristic X-rays may be used to identify the element from which they are being emitted. Can continuous X-rays be used for this purpose?

Why is exposure to X-rays injurious to health but not exposure to visible light, when both are electromagnetic waves?

An X-ray beam can be deflected

Consider a photon of a continuous X-ray coming from a Coolidge tube. Its energy comes from

The energy of a photon of a characteristic X-ray from a Coolidge tube comes from

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

If the current in the circuit for heating the filament is increased, the cutoff wavelength

Moseley's Law for characteristic X-ray is √v = a(Z − b). Here,

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 ?

The X-ray beam emerging from an X-ray tube

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?

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,

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

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

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

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

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.

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.

Mark the correct options.
(a) An atom with a vacancy has smaller energy that a neutral atom.
(b) K X-ray is emitted when a hole makes a jump from the K shell to some other shell.
(c) The wavelength of K X-ray is smaller than the wavelength of L X-ray of the same material.
(d) The wavelength of K_α X-ray is smaller than the wavelength of K_β X-ray of the same material.

For a given material, the energy and wavelength of characteristic X-rays satisfy
(a) E(K_α) > E(K_β) > E(K_γ)
(b) E(M_α) > E(L_α) > E(K_α)
(c) λ(K_α) > λ(K_β) > λ(K_γ)
(d) λ(M_α) > λ(L_α) > λ(K_α).

The potential difference applied to an X-ray tube is increased. As a result, in the emitted radiation,
(a) the intensity increases
(b) the minimum wavelength increases
(c) the intensity remains unchanged
(d) the minimum wavelength decreases.

When an electron strikes the target in a Coolidge tube, its entire kinetic energy
(a) is converted into a photon
(b) may be converted into a photon
(c) is converted into heat
(d) may be converted into heat.

X-ray incident on a material
(a) exerts a force on it
(b) transfers energy to it
(c) transfers momentum to it
(d) transfers impulse to it.

Consider a photon of continuous X-ray and a photon of characteristic X-ray of the same wavelength. Which of the following is/are different for the two photons?

Iron emits K_α X-ray of energy 6.4 keV. Calculate the times taken by an iron K_α photon to cross through a distance of 3 km.

(Use Planck constant h = 4.14 × 10^-15 eVs, speed of light c = 3 × 10⁸ m/s.)

Find the cutoff wavelength for the continuous X-rays coming from an X-ray tube operating at 30 kV.

(Use Planck constant h = 4.14 × 10^-15 eVs, speed of light c = 3 × 10⁸ m/s.)

What potential difference should be applied across an X-ray tube to get X-ray of wavelength not less than 0.10 nm? What is the maximum energy of a photon of this X-ray in joule?

(Use Planck constant h = 6.63 × 10^-34 Js= 4.14 × 10^-15 eVs, speed of light c = 3 × 10⁸ m/s.)

The X-ray coming from a Coolidge tube has a cutoff wavelength of 80 pm. Find the kinetic energy of the electrons hitting the target.

(Use Planck constant h = 6.63 × 10^-34 Js= 4.14 × 10^-15 eVs, speed of light c = 3 × 10⁸ m/s.)

If the operating potential in an X-ray tube is increased by 1%, by what percentage does the cutoff wavelength decrease?

(Use Planck constant h = 6.63 × 10^-34 Js= 4.14 × 10^-15 eVs, speed of light c = 3 × 10⁸ m/s.)

The distance between the cathode (filament) and the target in an X-ray tube is 1.5 m. If the cutoff wavelength is 30 pm, find the electric field between the cathode and the target.

(Use Planck constant h = 6.63 × 10^-34 Js= 4.14 × 10^-15 eVs, speed of light c = 3 × 10⁸ m/s.)

The short-wavelength limit shifts by 26 pm when the operating voltage in an X-ray tube is increased to 1.5 times the original value. What was the original value of the operating voltage?

(Use Planck constant h = 6.63 × 10^-34 Js= 4.14 × 10^-15 eVs, speed of light c = 3 × 10⁸ m/s.)

The electron beam in a colour TV is accelerated through 32 kV and then strikes the screen. What is the wavelength of the most energetic X-ray photon?

(Use Planck constant h = 6.63 × 10^-34 Js= 4.14 × 10^-15 eVs, speed of light c = 3 × 10⁸ m/s.)

The wavelength of K_α X-ray of tungsten is 21.3 pm. It takes 11.3 keV to knock out an electron from the L shell of a tungsten atom. What should be the minimum accelerating voltage across an X-ray tube having tungsten target which allows production of K_α X-ray?

(Use Planck constant h = 6.63 × 10^-34 Js= 4.14 × 10^-15 eVs, speed of light c = 3 × 10⁸ m/s.)

The K_β X-ray of argon has a wavelength of 0.36 nm. The minimum energy needed to ionize an argon atom is 16 eV. Find the energy needed to knock out an electron from the K shell of an argon atom.

The K_α X-rays of aluminium (Z = 13) and zinc (Z = 30) have wavelengths 887 pm and 146 pm respectively. Use Moseley's  law √v = a(Z − b) to find the wavelengths of the K_α X-ray of iron (Z = 26).

(Use Planck constant h = 6.63 × 10^-34 Js= 4.14 × 10^-15 eVs, speed of light c = 3 × 10⁸ m/s.)

A certain element emits K_α X-ray of energy 3.69 keV. Use the data from the previous problem to identify the element.

(Use Planck constant h = 6.63 × 10^-34 Js= 4.14 × 10^-15 eVs, speed of light c = 3 × 10⁸ m/s.)

The K_β X-rays from certain elements are given below. Draw a Moseley-type plot of √v versus Z for K_β radiation.

The K_α and K_β X-rays of molybdenum have wavelengths 0.71 A and 0.63 A respectively. Find the wavelength of L_α X-ray of molybdenum.

The K_α and K_β X-rays of molybdenum have wavelengths 0.71 A and 0.63 A respectively. Find the wavelength of L_α X-ray of molybdenum.

(Use Planck constant h = 6.63 × 10^-34 Js= 4.14 × 10^-15 eVs, speed of light c = 3 × 10⁸ m/s.)

The wavelengths of K_α and L_α X-rays of a material are 21.3 pm and 141 pm respectively. Find the wavelength of K_β X-ray of the material.

(Use Planck constant h = 6.63 × 10^-34 Js= 4.14 × 10^-15 eVs, speed of light c = 3 × 10⁸ m/s.)

The energy of a silver atom with a vacancy in K shell is 25.31 keV, in L shell is 3.56 keV and in M shell is 0.530 keV higher than the energy of the atom with no vacancy. Find the frequency of K_α, K_β and L_α X-rays of silver.

(Use Planck constant h = 6.63 × 10^-34 Js= 4.14 × 10^-15 eVs, speed of light c = 3 × 10⁸ m/s.)

Find the maximum potential difference which may be applied across an X-ray tube with tungsten target without emitting any characteristic K or L X-ray. The energy levels of the tungsten atom with an electron knocked out are as follows.

The electric current in an X-ray tube (from the target to the filament) operating at 40 kV is 10 mA. Assume that on an average, 1% of the total kinetic energy of the electron hitting hte target are converted into X-rays.
(a) What is the total power emitted as X-rays and (b) how much heat is produced in the target every second?

Heat at the rate of 200 W is produced in an X-ray tube operating at 20 kV. Find the current in the circuit. Assume that only a small fraction of the kinetic energy of electrons is converted into X-rays.

Continuous X-rays are made to strike a tissue paper soaked with polluted water. The incoming X-rays excite the atoms of the sample by knocking out the electrons from the inner shells. Characteristic X-rays are analysed and the intensity is plotted against the wavelength. Assuming that only K_α intensities are detected, list the elements present in the sample from the plot. Use Moseley's equation v − (25 × 10¹⁴Hz)(Z − 1)².

(Use Planck constant h = 6.63 × 10^-34 Js= 4.14 × 10^-15 eVs, speed of light c = 3 × 10⁸ m/s.)

A free atom of iron emits K_α X-rays of energy 6.4 keV. Calculate the recoil kinetic energy of the atom. Mass of an iron atom = 9.3 × 10⁻²⁶ kg.

(Use Planck constant h = 6.63 × 10^-34 Js= 4.14 × 10^-15 eVs, speed of light c = 3 × 10⁸ m/s.)

The stopping potential in a photoelectric experiment is linearly related to the inverse of the wavelength (1/λ) of the light falling on the cathode. The potential difference applied across an X-ray tube is linearly related to the inverse of the cutoff wavelength (1/λ) of the X-ray emitted. Show that the slopes of the lines in the two cases are equal and find its value.

(Use Planck constant h = 6.63 × 10^-34 Js= 4.14 × 10^-15 eVs, speed of light c = 3 × 10⁸ m/s.)

Suppose a monochromatic X-ray beam of wavelength 100 pm is sent through a Young's double slit and the interference pattern is observed on a photographic plate placed 40 cm away from the slit. What should be the separation between the slits so that the successive maxima on the screen are separated by a distance of 0.1 mm?