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.
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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