The β-decay process, discovered around 1900, is basically the decay of a neutron (n). In the laboratory, a proton (p) and an electron (e−) are observed as the decay products of the neutron. Therefore, considering the decay of a neutron as a two-body decay process, it was predicted theoretically that the kinetic energy of the electron should be a constant. But experimentally, it was observed that the electron kinetic energy has a continuous spectrum. Considering a three-body decay process, i.e. n→p+e−+¯¯¯ve, around 1930, Pauli explained the observed electron energy spectrum. Assuming the anti-neutrino (¯¯¯ve) to be massless and possessing negligible energy, and the neutron to be at rest, momentum and energy conservation principles are applied. From this calculation, the maximum kinetic energy of the electron is 0.8×106eV. The kinetic energy carried by the proton is only the recoil energy. If the anti-neutrino had a mass of 3 eV/c2 (where c is the speed of light) instead of zero mass, what should be the range of the kinetic energy, K, of the electron?
0≤K≤0.8×106eV
3.0eV≤K≤0.8×106cV
3.0eV≤K<0.8×106eV
0≤K<0.8×106eV
A
3.0eV≤K≤0.8×106cV
B
0≤K<0.8×106eV
C
0≤K≤0.8×106eV
D
3.0eV≤K<0.8×106eV
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Solution
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K can't be equal to 0.8×106eV as anti-neutrino must have some energy
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Q1
The β-decay process, discovered around 1900, is basically the decay of a neutron (n). In the laboratory, a proton (p) and an electron (e−) are observed as the decay products of the neutron. Therefore, considering the decay of a neutron as a two-body decay process, it was predicted theoretically that the kinetic energy of the electron should be a constant. But experimentally, it was observed that the electron kinetic energy has a continuous spectrum. Considering a three-body decay process, i.e. n→p+e−+¯¯¯ve, around 1930, Pauli explained the observed electron energy spectrum. Assuming the anti-neutrino (¯¯¯ve) to be massless and possessing negligible energy, and the neutron to be at rest, momentum and energy conservation principles are applied. From this calculation, the maximum kinetic energy of the electron is 0.8×106eV. The kinetic energy carried by the proton is only the recoil energy. If the anti-neutrino had a mass of 3 eV/c2 (where c is the speed of light) instead of zero mass, what should be the range of the kinetic energy, K, of the electron?
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Q2
Consider
the decay of a free neutron at rest: n
→p+ e–
Show
that the two-body decay of this type must necessarily give an
electron of fixed energy and, therefore, cannot account for the
observed continuous energy distribution in the β-decay
of a neutron or a nucleus (Fig. 6.19).
[Note:
The simple result of
this exercise was one among the several arguments advanced by W.
Pauli to predict the existence of a third particle in the decay
products of β-decay.
This particle is known as neutrino. We now know that it is a particle
of intrinsic spin ½ (like e–,
p or
n),
but is neutral, and either massless or having an extremely small mass
(compared to the mass of electron) and which interacts very weakly
with matter. The correct decay process of neutron is: n
→p + e–+ ν]