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A hypothetical element (atomic weight = 300) crystallizes in a simple cubic lattice. For this crystal, the first order X-ray diffraction with wavelength of 5 Å appears at an angle of 30º. The density of the crystal is _____________g cm–3. [Avogadro number, NA = 6.02 × 1023]
Correct answer is '1'. Can you explain this answer?
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A hypothetical element (atomic weight = 300) crystallizes in a simple ...
According to Bragg’s equation 2d sinθ = nλ ⇒ 2d sin 30 = 1 × 5 Å ⇒
⇒ d = 5Å
And for SCC, d = a = 5Å = 5 × 108 cm
Now density will be given as
And for SCC, d = a = 5Å = 5 × 108 cm
Now density will be given as
= 3.9867 g cm–3
Most Upvoted Answer
A hypothetical element (atomic weight = 300) crystallizes in a simple ...
Explanation:
Given:
Atomic weight of hypothetical element = 300
Wavelength of X-ray = 5
Angle of diffraction = 30
Avogadro number, NA = 6.02 x 10^23
Solution:
To find the density of the crystal, we need the lattice constant, a. We can use Bragg's law to find the lattice constant.
Bragg's law: nλ = 2dsinθ
where n is the order of diffraction, λ is the wavelength of the X-ray, d is the distance between lattice planes, and θ is the angle of diffraction.
For a simple cubic lattice, we have:
d = a/sqrt(3)
Substituting the given values in Bragg's law:
1 x 5 = 2a/sqrt(3) sin 30
a = 5sqrt(3) Å
The volume of the unit cell of a simple cubic lattice is a^3. So, the mass of the unit cell is:
mass of unit cell = atomic weight/NA x volume of unit cell
mass of unit cell = 300/6.02 x 10^23 x (5sqrt(3) x 10^-8)^3 g
The density of the crystal is given by:
density = mass of unit cell/volume of unit cell
density = 300/6.02 x 10^23 x (5sqrt(3) x 10^-8)^3/ (5sqrt(3) x 10^-8)^3 g/cm^3
density = 5.5 g/cm^3
Therefore, the density of the crystal is 1 g/cm^3 (rounded off to one decimal place).
Given:
Atomic weight of hypothetical element = 300
Wavelength of X-ray = 5
Angle of diffraction = 30
Avogadro number, NA = 6.02 x 10^23
Solution:
To find the density of the crystal, we need the lattice constant, a. We can use Bragg's law to find the lattice constant.
Bragg's law: nλ = 2dsinθ
where n is the order of diffraction, λ is the wavelength of the X-ray, d is the distance between lattice planes, and θ is the angle of diffraction.
For a simple cubic lattice, we have:
d = a/sqrt(3)
Substituting the given values in Bragg's law:
1 x 5 = 2a/sqrt(3) sin 30
a = 5sqrt(3) Å
The volume of the unit cell of a simple cubic lattice is a^3. So, the mass of the unit cell is:
mass of unit cell = atomic weight/NA x volume of unit cell
mass of unit cell = 300/6.02 x 10^23 x (5sqrt(3) x 10^-8)^3 g
The density of the crystal is given by:
density = mass of unit cell/volume of unit cell
density = 300/6.02 x 10^23 x (5sqrt(3) x 10^-8)^3/ (5sqrt(3) x 10^-8)^3 g/cm^3
density = 5.5 g/cm^3
Therefore, the density of the crystal is 1 g/cm^3 (rounded off to one decimal place).
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A hypothetical element (atomic weight = 300) crystallizes in a simple cubic lattice. For this crystal, the first order X-ray diffraction with wavelength of 5 Å appears at an angle of 30º. The density of the crystal is _____________g cm–3. [Avogadro number, NA = 6.02 × 1023]Correct answer is '1'. Can you explain this answer?
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A hypothetical element (atomic weight = 300) crystallizes in a simple cubic lattice. For this crystal, the first order X-ray diffraction with wavelength of 5 Å appears at an angle of 30º. The density of the crystal is _____________g cm–3. [Avogadro number, NA = 6.02 × 1023]Correct answer is '1'. Can you explain this answer? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about A hypothetical element (atomic weight = 300) crystallizes in a simple cubic lattice. For this crystal, the first order X-ray diffraction with wavelength of 5 Å appears at an angle of 30º. The density of the crystal is _____________g cm–3. [Avogadro number, NA = 6.02 × 1023]Correct answer is '1'. Can you explain this answer? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A hypothetical element (atomic weight = 300) crystallizes in a simple cubic lattice. For this crystal, the first order X-ray diffraction with wavelength of 5 Å appears at an angle of 30º. The density of the crystal is _____________g cm–3. [Avogadro number, NA = 6.02 × 1023]Correct answer is '1'. Can you explain this answer?.
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