Advertisements
Advertisements
Question
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 Kα, Kβ and Lα 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.)
Advertisements
Solution
Given:-
Energy of electron in the K shell, Ek = 25.31 keV
Energy of electron in the L shell, EL = 3.56 keV
Energy of electron in the M shell, EM = 0.530 keV
Let f be the frequency of Kα X-ray and f0 be the frequency of Kβ X-ray.
Let f1 be the frequency of Lα X-rays of silver.
∴ Kα = EK − EL = hf
Here, h = Planck constant
f = frequency of `Kα` X-ray
`f = (E_K - E_L)/h`
`f = ((25.31 xx 3.56))/(6.63 xx 10^-34) xx 1.6 xx 10^-19 xx 10^3`
`f = (21.75 xx 10^3 xx 10^15)/6.67`
`f = 5.25 xx 10^18 "Hz"`
`K_β = E_K - E_M = hf_0`
`⇒ f_0 = (E_K - E_M)/h`
`⇒ f_0 = ((25.31 - 0.53))/(6.67 xx 10^-34) xx 10^3 xx 1.6 xx 10^-19`
`⇒ f_0 = 5.985 xx 10^18 "Hz"`
`K_L = E_L - E_M = hf_1`
`f_1 = (E_L - E_M)/h`
`f_1 = (3.56 - 0.530)/(6.63 xx 10^-34) xx 10^3 xx 1.6 xx 10^-19`
`f_1 = 7.32 xx 10^17 "Hz"`
APPEARS IN
RELATED QUESTIONS
Name the parts of the electromagnetic spectrum which is
used to treat muscular strain.
Write in brief, how these waves can be produced.
What physical quantity is the same for X-rays of wavelength 10−10 m, red light of wavelength 6800 Å and radiowaves of wavelength 500 m?
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)].
Name the electromagnetic radiations used for (a) water purification, and (b) eye surgery.
Can X-rays be used for photoelectric effect?
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 VA and the atomic number of the target material is ZA. These quantities are VB and ZB 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
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
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 Kα X-ray is smaller than the wavelength of Kβ X-ray of the same material.
Iron emits Kα X-ray of energy 6.4 keV. Calculate the times taken by an iron Kα 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.)
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.)
Define the term "Intensity" in the photon picture of electromagnetic radiation.
Choose the correct option.
How does the frequency of a beam of ultraviolet light change when it travels from air into glass?
Name the e.m. waves which are suitable for radar systems used in aircraft navigation. Write the range of frequency of these waves.
For television broadcasting, the frequency employed is normally
SONAR emits which of the following waves?
All components of the electromagnetic spectrum in a vacuum have the same ______
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.
Identify the electromagnetic wave whose wavelength range is from about 10-3 m to about 10-1 m. Write one use of this.
What happens when an electron collides with a positron?
