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A particle X moving with a certain velocity has a de Broglie wavelength of 1 Angstrom. If particle Y has a mass of 25% that of X and velocity 75% that if X, de Broglie wavelength of Y will be a)3 angstrom b)5.33 Angstrom c)6.88 Angstrom d)48angstrom?
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A particle X moving with a certain velocity has a de Broglie wavelengt...
Solution:
De Broglie Wavelength Formula:
The de Broglie wavelength of a particle is given by the formula:
λ = h/p
where λ is the de Broglie wavelength, h is the Planck constant, and p is the momentum of the particle.
Relation between Mass, Velocity and Momentum:
The momentum of a particle is given by the formula:
p = mv
where p is the momentum, m is the mass, and v is the velocity of the particle.
Relation between De Broglie Wavelength, Mass, and Velocity:
Substituting the value of momentum in the de Broglie wavelength formula, we get:
λ = h/mv
Multiplying and dividing the numerator by the velocity of light (c), we get:
λ = h/mc * c/v
Since c is a constant, we can write h/mc as a constant and get:
λ = h/mc * 1/v
This formula shows that the de Broglie wavelength of a particle is inversely proportional to its velocity and directly proportional to its mass.
Calculations:
Let the de Broglie wavelength of particle X be λX.
λX = h/pX
Let the de Broglie wavelength of particle Y be λY.
λY = h/pY
We are given that:
mY = 0.25mX
vY = 0.75vX
Substituting the values of mass and velocity in the formula for momentum, we get:
pY = mYvY = 0.25mX * 0.75vX = 0.1875mXvX
Substituting the value of momentum in the formula for de Broglie wavelength, we get:
λY = h/pY = h/0.1875mXvX
Substituting the value of λX in terms of pX, we get:
λX = h/pX = h/mXvX
Dividing λY by λX, we get:
λY/λX = (h/0.1875mXvX)/(h/mXvX) = 0.1875
Multiplying both sides by λX, we get:
λY = 0.1875λX
Substituting the value of λX, we get:
λY = 0.1875 * 1 Angstrom = 0.1875 Angstrom
Therefore, the de Broglie wavelength of particle Y is 0.1875 Angstrom or 1.88 * 10^-10 meters.
Answer:
Option (d) 48 Angstrom is not correct.
The correct answer is (b) 5.33 Angstrom.
De Broglie Wavelength Formula:
The de Broglie wavelength of a particle is given by the formula:
λ = h/p
where λ is the de Broglie wavelength, h is the Planck constant, and p is the momentum of the particle.
Relation between Mass, Velocity and Momentum:
The momentum of a particle is given by the formula:
p = mv
where p is the momentum, m is the mass, and v is the velocity of the particle.
Relation between De Broglie Wavelength, Mass, and Velocity:
Substituting the value of momentum in the de Broglie wavelength formula, we get:
λ = h/mv
Multiplying and dividing the numerator by the velocity of light (c), we get:
λ = h/mc * c/v
Since c is a constant, we can write h/mc as a constant and get:
λ = h/mc * 1/v
This formula shows that the de Broglie wavelength of a particle is inversely proportional to its velocity and directly proportional to its mass.
Calculations:
Let the de Broglie wavelength of particle X be λX.
λX = h/pX
Let the de Broglie wavelength of particle Y be λY.
λY = h/pY
We are given that:
mY = 0.25mX
vY = 0.75vX
Substituting the values of mass and velocity in the formula for momentum, we get:
pY = mYvY = 0.25mX * 0.75vX = 0.1875mXvX
Substituting the value of momentum in the formula for de Broglie wavelength, we get:
λY = h/pY = h/0.1875mXvX
Substituting the value of λX in terms of pX, we get:
λX = h/pX = h/mXvX
Dividing λY by λX, we get:
λY/λX = (h/0.1875mXvX)/(h/mXvX) = 0.1875
Multiplying both sides by λX, we get:
λY = 0.1875λX
Substituting the value of λX, we get:
λY = 0.1875 * 1 Angstrom = 0.1875 Angstrom
Therefore, the de Broglie wavelength of particle Y is 0.1875 Angstrom or 1.88 * 10^-10 meters.
Answer:
Option (d) 48 Angstrom is not correct.
The correct answer is (b) 5.33 Angstrom.
Community Answer
A particle X moving with a certain velocity has a de Broglie wavelengt...
B)5.33A.we know, wavelength=h/mv..for X particle ,wavelength1beXparticlewavelength=1A.mass of X is m.velocity of X is V.for Y particle ,mass2 be mass of Y particle =25% m.=25/100m.velocity2 be velocity of Y particle =75%v.=75/100v.wavelength 2 be Y particle wavelength.wavelength 2/wavelength 1=m1v1/m2v2.wavelength 2/1A=100×100/25×75.wavelength 2=4×4 A /3.Wavelength 2=16 A /3.wavelength 2= 5.33A.
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A particle X moving with a certain velocity has a de Broglie wavelength of 1 Angstrom. If particle Y has a mass of 25% that of X and velocity 75% that if X, de Broglie wavelength of Y will be a)3 angstrom b)5.33 Angstrom c)6.88 Angstrom d)48angstrom?
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A particle X moving with a certain velocity has a de Broglie wavelength of 1 Angstrom. If particle Y has a mass of 25% that of X and velocity 75% that if X, de Broglie wavelength of Y will be a)3 angstrom b)5.33 Angstrom c)6.88 Angstrom d)48angstrom? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A particle X moving with a certain velocity has a de Broglie wavelength of 1 Angstrom. If particle Y has a mass of 25% that of X and velocity 75% that if X, de Broglie wavelength of Y will be a)3 angstrom b)5.33 Angstrom c)6.88 Angstrom d)48angstrom? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle X moving with a certain velocity has a de Broglie wavelength of 1 Angstrom. If particle Y has a mass of 25% that of X and velocity 75% that if X, de Broglie wavelength of Y will be a)3 angstrom b)5.33 Angstrom c)6.88 Angstrom d)48angstrom?.
A particle X moving with a certain velocity has a de Broglie wavelength of 1 Angstrom. If particle Y has a mass of 25% that of X and velocity 75% that if X, de Broglie wavelength of Y will be a)3 angstrom b)5.33 Angstrom c)6.88 Angstrom d)48angstrom? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A particle X moving with a certain velocity has a de Broglie wavelength of 1 Angstrom. If particle Y has a mass of 25% that of X and velocity 75% that if X, de Broglie wavelength of Y will be a)3 angstrom b)5.33 Angstrom c)6.88 Angstrom d)48angstrom? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle X moving with a certain velocity has a de Broglie wavelength of 1 Angstrom. If particle Y has a mass of 25% that of X and velocity 75% that if X, de Broglie wavelength of Y will be a)3 angstrom b)5.33 Angstrom c)6.88 Angstrom d)48angstrom?.
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