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The density of copper (Cu) is 8.90 g/m3 with contribution of 1 electron/atom. The plasma frequency of copper is_______x 1016 /s. (Given atomic weight = 63.5)(Round off to one decimal place)
Correct answer is between '1.5,1.7'. Can you explain this answer?
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The density of copper (Cu) is 8.90 g/m3 with contribution of 1 electro...
n = concentration of free electron
and for electron,
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The density of copper (Cu) is 8.90 g/m3 with contribution of 1 electro...
Calculation of Plasma Frequency of Copper
Density of Copper
- Given density of copper = 8.90 g/m^3
Contribution of Electron/Atom
- Given contribution of electron/atom = 1
Atomic Weight of Copper
- Given atomic weight of copper = 63.5
Formula for Plasma Frequency
The formula for plasma frequency is given by:
ωp = √(ne^2 / ε0m)
where,
- ωp = Plasma frequency
- n = Number density of electrons
- e = Charge of electron
- ε0 = Permittivity of free space
- m = Mass of electron
Number Density of Electrons
Number density of electrons can be calculated using the following formula:
n = ρN / M
where,
- N = Avogadro's number = 6.022 x 10^23 atoms/mol
- M = Atomic weight of copper = 63.5 g/mol
- ρ = Density of copper = 8.90 g/m^3
By substituting the given values in the formula, we get:
n = (8.90 g/m^3 x 6.022 x 10^23 atoms/mol) / 63.5 g/mol
n = 8.39 x 10^22 electrons/m^3
Plasma Frequency of Copper
Now, we can substitute the calculated values in the plasma frequency formula:
ωp = √(ne^2 / ε0m)
ωp = √((8.39 x 10^22 electrons/m^3 x (1.602 x 10^-19 C)^2) / (8.854 x 10^-12 F/m x 9.109 x 10^-31 kg))
ωp = 1.67 x 10^16 /s
Rounding off the answer to one decimal place, we get:
Plasma frequency of copper = 1.7 x 10^16 /s
Therefore, the correct answer falls between 1.5 and 1.7 x 10^16 /s.
Density of Copper
- Given density of copper = 8.90 g/m^3
Contribution of Electron/Atom
- Given contribution of electron/atom = 1
Atomic Weight of Copper
- Given atomic weight of copper = 63.5
Formula for Plasma Frequency
The formula for plasma frequency is given by:
ωp = √(ne^2 / ε0m)
where,
- ωp = Plasma frequency
- n = Number density of electrons
- e = Charge of electron
- ε0 = Permittivity of free space
- m = Mass of electron
Number Density of Electrons
Number density of electrons can be calculated using the following formula:
n = ρN / M
where,
- N = Avogadro's number = 6.022 x 10^23 atoms/mol
- M = Atomic weight of copper = 63.5 g/mol
- ρ = Density of copper = 8.90 g/m^3
By substituting the given values in the formula, we get:
n = (8.90 g/m^3 x 6.022 x 10^23 atoms/mol) / 63.5 g/mol
n = 8.39 x 10^22 electrons/m^3
Plasma Frequency of Copper
Now, we can substitute the calculated values in the plasma frequency formula:
ωp = √(ne^2 / ε0m)
ωp = √((8.39 x 10^22 electrons/m^3 x (1.602 x 10^-19 C)^2) / (8.854 x 10^-12 F/m x 9.109 x 10^-31 kg))
ωp = 1.67 x 10^16 /s
Rounding off the answer to one decimal place, we get:
Plasma frequency of copper = 1.7 x 10^16 /s
Therefore, the correct answer falls between 1.5 and 1.7 x 10^16 /s.
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The density of copper (Cu) is 8.90 g/m3 with contribution of 1 electron/atom. The plasma frequency of copper is_______x 1016 /s. (Given atomic weight = 63.5)(Round off to one decimal place)Correct answer is between '1.5,1.7'. Can you explain this answer?
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The density of copper (Cu) is 8.90 g/m3 with contribution of 1 electron/atom. The plasma frequency of copper is_______x 1016 /s. (Given atomic weight = 63.5)(Round off to one decimal place)Correct answer is between '1.5,1.7'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The density of copper (Cu) is 8.90 g/m3 with contribution of 1 electron/atom. The plasma frequency of copper is_______x 1016 /s. (Given atomic weight = 63.5)(Round off to one decimal place)Correct answer is between '1.5,1.7'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The density of copper (Cu) is 8.90 g/m3 with contribution of 1 electron/atom. The plasma frequency of copper is_______x 1016 /s. (Given atomic weight = 63.5)(Round off to one decimal place)Correct answer is between '1.5,1.7'. Can you explain this answer?.
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