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A particle of mass M at rest decays into two particles of masses m1 and m2, having nonzero velocities. The ratio of the de Broglie wavelength of the particles λ 1 / λ 2 is
- a)m1/m2
- b)m2/m1
- c)1.0
- d)√m2 √m1
Correct answer is option 'C'. Can you explain this answer?
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A particle of mass M at rest decays into two particles of masses m1 an...
The de Broglie wavelength is given by the equation λ = h/p, where λ is the wavelength, h is Planck's constant, and p is the momentum of the particle.
In this case, the initial particle has zero momentum (since it is at rest), so its de Broglie wavelength is undefined. However, we can calculate the de Broglie wavelengths of the two particles that it decays into.
Let v1 and v2 be the velocities of the two particles after the decay. Then, their momenta are given by p1 = m1v1 and p2 = m2v2. Using the de Broglie equation, we have:
λ1 = h/p1 = h/(m1v1)
λ2 = h/p2 = h/(m2v2)
Taking the ratio of these two wavelengths, we get:
λ1/λ2 = (m2v2)/(m1v1)
Note that this ratio depends on the masses and velocities of the two particles, and not on the mass of the original particle.
In this case, the initial particle has zero momentum (since it is at rest), so its de Broglie wavelength is undefined. However, we can calculate the de Broglie wavelengths of the two particles that it decays into.
Let v1 and v2 be the velocities of the two particles after the decay. Then, their momenta are given by p1 = m1v1 and p2 = m2v2. Using the de Broglie equation, we have:
λ1 = h/p1 = h/(m1v1)
λ2 = h/p2 = h/(m2v2)
Taking the ratio of these two wavelengths, we get:
λ1/λ2 = (m2v2)/(m1v1)
Note that this ratio depends on the masses and velocities of the two particles, and not on the mass of the original particle.
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A particle of mass M at rest decays into two particles of masses m1 and m2, having nonzero velocities. The ratio of the de Broglie wavelength of the particles λ 1 / λ 2 isa)m1/m2b)m2/m1c)1.0d)√m2√m1Correct answer is option 'C'. Can you explain this answer?
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