Advertisements
Advertisements
प्रश्न
An X-ray tube operates at 40 kV. Suppose the electron converts 70% of its energy into a photon at each collision. Find the lowest there wavelengths emitted from the tube. Neglect the energy imparted to the atom with which the electron collides.
(Use Planck constant h = 6.63 × 10-34 Js= 4.14 × 10-15 eVs, speed of light c = 3 × 108 m/s.)
Advertisements
उत्तर
Given:-
Potential of the X-ray tube, V = 40 kV = 40 × 103 V
Energy = 40 × 103 eV
Energy utilised by the electron is given by `E = 70/100 xx 40 xx 10^3 = 28 xx 10^3 "eV"`
Wavelength (`lambda`) is given by
`lambda = (hc)/E`
Here,
h = Planck's constant
c = Speed of light
E = Energy of the electron
`therefore lambda = (hc)/E`
`⇒ lambda = (1242 "eV" - "nm")/(28 xx 10^3 "eV")`
`⇒ lambda = (1242 xx 10^-9 "eV")/(28 xx 10^3 "eV")`
`⇒ lambda = 44.35 xx 10^-12`
`⇒ lambda = 44.35 "pm"`
For the second wavelength,
E = 70% (Leftover energy)
`= 70/100 xx (40-28)10^3`
`= 70/100 xx 12 xx 10^3`
`= 84 xx 10^2 "eV"`
And
`lambda = (hc)/E = 1242/(8.4 xx 10^3)`
`= 147.86 xx 10^-3 "nm"`
`= 147.86 "pm" = 148 "pm"`
For the third wavelength,
`E = 70/100(12 - 8.4) xx 10^3`
`= 7 xx 3.6 xx 10^2 = 25.2 xx 10^2 "eV"`
And ,
`lambda = (hc)/E = 1242/(25.2 xx 10^2)`
`= 49.2857 xx 10^-2`
`= 493 "pm"`
APPEARS IN
संबंधित प्रश्न
Given below are some famous numbers associated with electromagnetic radiations in different contexts in physics. State the part of the electromagnetic spectrum to which each belongs.
(a) 21 cm (wavelength emitted by atomic hydrogen in interstellar space).
(b) 1057 MHz (frequency of radiation arising from two close energy levels in hydrogen; known as Lamb shift).
(c) 2.7 K [temperature associated with the isotropic radiation filling all space-thought to be a relic of the ‘big-bang’ origin of the universe].
(d) 5890 Å - 5896 Å [double lines of sodium]
(e) 14.4 keV [energy of a particular transition in 57Fe nucleus associated with a famous high resolution spectroscopic method (Mössbauer spectroscopy)].
The wavelengths for the light of red and blue colours are roughly 7.8 × `10^7` m and 4.8 × `10^7` m respectively.
(a) Which colour has the greater speed in vacuum?
(b) Which colour has the greater speed in glass?
Arrange the following radiations in the order of their increasing wavelength:
X-rays, infrared rays, ratio waves, gamma ray and microwaves.
Name the region beyond the violet end of the spectrum called.
Name the waves of wavelength nearly 0.1 nm.
Name three properties of ultraviolet radiations which are similar to visible light.
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?
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
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.)
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?
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 Kα 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.)
Name the scientist who discovered
X-rays
Name the radiation which can be detected by thermopile.
Name any two electromagnetic waves which have a frequency higher than that of violet light. State one use of each.
Choose the correct option.
The EM wave emitted by the Sun and responsible for heating the Earth’s atmosphere due to greenhouse effect is
Solve the numerical problem.
The speed of light is 3 × 108 m/s. Calculate the frequency of red light of a wavelength of 6.5 × 10−7 m.
For television broadcasting, the frequency employed is normally
The half-value thickness of an absorber is defined as the thickness that will reduce exponentially the intensity of a beam of particles by a factor of 2. The half-value thickness in (µm) for lead assuming X-ray beam of wavelength 20 pm, µ = 50 cm-1 for X-rays in lead at wavelength λ = 20 pm, is ______ µm.
Which is the correct ascending order of wavelengths?
Photons of an electromagnetic radiation has an energy 11 keV each. To which region of electromagnetic spectrum does it belong?
