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A particle with zero mass (a neutrino, possibly) can transport momentum. However, by Eq. 20-23, the momentum is directly proportional to the mass and therefore should be zero if the mass is zero. Explain.

A particle with zero mass (a neutrino, possibly) can transport momentum. However, by Eq. 20-23, the momentum is directly proportional to the mass and therefore should be zero if the mass is zero. Explain.

Grade:11

1 Answers

Kevin Nash
askIITians Faculty 332 Points
8 years ago
Neutrino is not a classical particle. It is a relativistic quantum particle. For a relativistic quantum particle, momentum (p) is defined as
p = E /c
Here E is the relativistic energy of the particle and c is the speed of the light.
The emitted neutrino has energy associated with it. This means it can have momentum.
Again we know that,
E = hf
Here, h is the Planck’s constant and f is the frequency of the particle.
To obtain momentum (p) of the neutrino, substitute hf for energy E in the equation
p = E /c,
p = E /c
= hf /c
= h/λ (Since, speed of light (c) = frequency (f) × wavelength (λ))
Therefore measuring wavelength λ of the neutrino you can obtain the momentum of the neutrino despite of that zero mass.

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