Advertisements
Advertisements
Question
The Kα and Kβ X-rays of molybdenum have wavelengths 0.71 A and 0.63 A respectively. Find the wavelength of Lα X-ray of molybdenum.
Advertisements
Solution
Given :
Wavelength of Kα X-rays, `lambda_1`= 0.71 A
Wavelength of Kβ X-rays, `lambda_2` = 0.63 A
For La X-ray of molybdenum,
a = 57
b = 1
From Moseley's equation,
`sqrt(v) = a(Z - b)`
Here, v = frequency of X-ray
Z = atomic number of the element
`sqrt(v) = a(Z - b)`
⇒ `sqrt(v) = a(57 - 1)`
= `a xx 56` ...(1)
For `Cu` (29),
`sqrt(1.88 xx 10^18) = a(29 - 1) = 28 a ...(2)`
Dividing (1) and (2)
`sqrt(v/(1.88 xx 10^18)) = (a xx 56)/(a xx 28) = 2`
⇒ `v = 1.88 xx 10^18 xx (2)^2`
= `4 xx 1.88 xx 10^18`
= `7.52 xx 10^18 "Hz"`
APPEARS IN
RELATED QUESTIONS
How are infrared waves produced?
To which part of electromagnetic spectrum does a wave of frequency 3 × 1013 Hz belong?
A plane electromagnetic wave travels in vacuum along z-direction. What can you say about the directions of its electric and magnetic field vectors? If the frequency of the wave is 30 MHz, what is its wavelength?
The small ozone layer on top of the stratosphere is crucial for human survival. Why?
Name the electromagnetic radiations used for (a) water purification, and (b) eye surgery.
Arrange the following radiations in the order of their increasing wavelength:
X-rays, infrared rays, ratio waves, gamma ray and microwaves.
A wave has a wavelength of 10-3 nm. Name the wave.
What is the range of the wavelength of the following electromagnetic waves?
(a) Ultraviolet
Name the waves of wavelength nearly 0.1 nm.
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?
A certain element emits Kα 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.)
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?
Name the scientist who discovered
X-rays
Name the scientist who discovered Ultraviolet rays
Arrange the following electromagnetic waves in increasing order of their frequencies (i.e. begin with the lowest frequency):
Visible light, y rays, X rays, microwaves, radio waves, infrared radiations, and ultraviolet radiation.
Answer briefly.
Why light waves travel in a vacuum whereas sound waves cannot?
Answer briefly.
What are radio waves?
Answer briefly.
Name the most harmful radiation entering the Earth's atmosphere from outer space.
Solve the numerical problem.
Calculate the frequency in MHz of a radio wave of wavelength 250 m. Remember that the speed of all EM waves in a vacuum is 3.0 × 108 m/s.
Electromagnetic waves of wavelengths λ1, λ2 and λ3 are used in a radar system, in water purifiers and in remote switches of TV, respectively.
- Identify the electromagnetic waves.
- Write one source for each of them.
