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The wavelength of the Lα x- rays spectral line of platinum (atomic number 78) is 1.321 Å. An unknown substance units Lα x- rays of wavelength 4.174 Å. Calculate the atomic number of the unknown substance. Given b = 7.4 for La line ?
Correct answer is '47'. Can you explain this answer?
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The wavelength of the Lα x- rays spectral line of platinum (atomi...
Given:
- Wavelength of L x-ray spectral line of platinum (Z=78) = 1.321 Å
- Wavelength of L x-ray spectral line of unknown substance = 4.174 Å
- b value for La line = 7.4
To find:
Atomic number (Z) of the unknown substance.
Explanation:
1. Understanding the concept of X-ray emission:
- X-rays are produced when high-energy electrons collide with atoms.
- These collisions cause inner shell electrons to be ejected from their orbits.
- When the inner shell is vacant, an electron from the outer shell fills this vacancy and emits an X-ray photon.
2. Moseley's Law:
- Moseley's law states that the square root of the frequency of the emitted X-ray is directly proportional to the atomic number (Z) of the element.
- Mathematically, it can be written as √ν = a(Z - b), where 'a' and 'b' are constants.
3. Using Moseley's Law to find atomic number:
- We are given the wavelength (λ) of the L x-ray spectral line for both platinum and the unknown substance.
- The frequency (ν) of the X-ray can be calculated using the equation c = λν, where c is the speed of light.
- Taking the square root of the frequency, we can rewrite the equation as: √(c/λ) = a(Z - b).
- Since the speed of light (c) and the constant 'a' are the same for both substances, we can equate the equations for platinum and the unknown substance.
4. Setting up the equation:
For platinum: √(c/1.321) = a(78 - b)
For unknown substance: √(c/4.174) = a(Z - b)
5. Solving for atomic number:
- Divide the equation for the unknown substance by the equation for platinum:
√(c/4.174) / √(c/1.321) = (a(Z - b))/(a(78 - b))
Simplifying, we get: √(1.321/4.174) = (Z - b) / (78 - b)
- Substitute the given value of 'b' (7.4) and solve for 'Z':
√(1.321/4.174) = (Z - 7.4) / (78 - 7.4)
Simplifying, we get: Z - 7.4 = 0.532(70.6)
Z - 7.4 = 37.6
Z = 37.6 + 7.4
Z = 45 + 2
Z = 47
Answer:
The atomic number of the unknown substance is 47.
- Wavelength of L x-ray spectral line of platinum (Z=78) = 1.321 Å
- Wavelength of L x-ray spectral line of unknown substance = 4.174 Å
- b value for La line = 7.4
To find:
Atomic number (Z) of the unknown substance.
Explanation:
1. Understanding the concept of X-ray emission:
- X-rays are produced when high-energy electrons collide with atoms.
- These collisions cause inner shell electrons to be ejected from their orbits.
- When the inner shell is vacant, an electron from the outer shell fills this vacancy and emits an X-ray photon.
2. Moseley's Law:
- Moseley's law states that the square root of the frequency of the emitted X-ray is directly proportional to the atomic number (Z) of the element.
- Mathematically, it can be written as √ν = a(Z - b), where 'a' and 'b' are constants.
3. Using Moseley's Law to find atomic number:
- We are given the wavelength (λ) of the L x-ray spectral line for both platinum and the unknown substance.
- The frequency (ν) of the X-ray can be calculated using the equation c = λν, where c is the speed of light.
- Taking the square root of the frequency, we can rewrite the equation as: √(c/λ) = a(Z - b).
- Since the speed of light (c) and the constant 'a' are the same for both substances, we can equate the equations for platinum and the unknown substance.
4. Setting up the equation:
For platinum: √(c/1.321) = a(78 - b)
For unknown substance: √(c/4.174) = a(Z - b)
5. Solving for atomic number:
- Divide the equation for the unknown substance by the equation for platinum:
√(c/4.174) / √(c/1.321) = (a(Z - b))/(a(78 - b))
Simplifying, we get: √(1.321/4.174) = (Z - b) / (78 - b)
- Substitute the given value of 'b' (7.4) and solve for 'Z':
√(1.321/4.174) = (Z - 7.4) / (78 - 7.4)
Simplifying, we get: Z - 7.4 = 0.532(70.6)
Z - 7.4 = 37.6
Z = 37.6 + 7.4
Z = 45 + 2
Z = 47
Answer:
The atomic number of the unknown substance is 47.
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The wavelength of the Lα x- rays spectral line of platinum (atomic number 78) is 1.321 Å. An unknown substance units Lαx- rays of wavelength 4.174 Å. Calculate the atomic number of the unknown substance. Given b = 7.4 for La line ?Correct answer is '47'. Can you explain this answer?
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The wavelength of the Lα x- rays spectral line of platinum (atomic number 78) is 1.321 Å. An unknown substance units Lαx- rays of wavelength 4.174 Å. Calculate the atomic number of the unknown substance. Given b = 7.4 for La line ?Correct answer is '47'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about The wavelength of the Lα x- rays spectral line of platinum (atomic number 78) is 1.321 Å. An unknown substance units Lαx- rays of wavelength 4.174 Å. Calculate the atomic number of the unknown substance. Given b = 7.4 for La line ?Correct answer is '47'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The wavelength of the Lα x- rays spectral line of platinum (atomic number 78) is 1.321 Å. An unknown substance units Lαx- rays of wavelength 4.174 Å. Calculate the atomic number of the unknown substance. Given b = 7.4 for La line ?Correct answer is '47'. Can you explain this answer?.
The wavelength of the Lα x- rays spectral line of platinum (atomic number 78) is 1.321 Å. An unknown substance units Lαx- rays of wavelength 4.174 Å. Calculate the atomic number of the unknown substance. Given b = 7.4 for La line ?Correct answer is '47'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about The wavelength of the Lα x- rays spectral line of platinum (atomic number 78) is 1.321 Å. An unknown substance units Lαx- rays of wavelength 4.174 Å. Calculate the atomic number of the unknown substance. Given b = 7.4 for La line ?Correct answer is '47'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The wavelength of the Lα x- rays spectral line of platinum (atomic number 78) is 1.321 Å. An unknown substance units Lαx- rays of wavelength 4.174 Å. Calculate the atomic number of the unknown substance. Given b = 7.4 for La line ?Correct answer is '47'. Can you explain this answer?.
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The wavelength of the Lα x- rays spectral line of platinum (atomic number 78) is 1.321 Å. An unknown substance units Lαx- rays of wavelength 4.174 Å. Calculate the atomic number of the unknown substance. Given b = 7.4 for La line ?Correct answer is '47'. Can you explain this answer?, a detailed solution for The wavelength of the Lα x- rays spectral line of platinum (atomic number 78) is 1.321 Å. An unknown substance units Lαx- rays of wavelength 4.174 Å. Calculate the atomic number of the unknown substance. Given b = 7.4 for La line ?Correct answer is '47'. Can you explain this answer? has been provided alongside types of The wavelength of the Lα x- rays spectral line of platinum (atomic number 78) is 1.321 Å. An unknown substance units Lαx- rays of wavelength 4.174 Å. Calculate the atomic number of the unknown substance. Given b = 7.4 for La line ?Correct answer is '47'. Can you explain this answer? theory, EduRev gives you an
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