During alpha-decay , a nucleus decays by emitting an `alpha`-particle ( a helium nucleus `._2He^4`) according to the equation
`._Z^AX to ._(Z-2)^(A-4)Y+._2^4He+Q`
In this process, the energy released Q is shared by the emitted `alpha`-particle and daughter nucleus in the form of kinetic energy .
The energy Q is divided in a definite ratio among the `alpha`-particle and the daughter nucleus .
A nucleus that decays spontaneously by emitting an electron or a positron is said to undergo `beta`-decay .This process also involves a release of definite energy . Initially, the `beta`-decay was represented as `._Z^AX to ._(Z+1)^AY + e^(-)"(electron)"+Q`
According to this reaction, the energy released during each decay must be divided in definite ratio by the emitted e' (`beta`-particle) and the daughter nucleus. While , in alpha decay, it has been found that every emitted `alpha`-particle has the same sharply defined kinetic energy. It is not so in case of `beta`-decay . The energy of emitted electrons or positrons is found to vary between zero to a certain maximum value. Wolfgang Pauli first suggested the existence of neutrinoes in 1930. He suggested that during `beta`-decay, a third particle is also emitted. It shares energy with the emitted `beta` particles and thus accounts for the energy distribution.
The beta particles (positron) are emitted with different kinetic energies because

Options

A. Neutrino shares a definite amount of energy with positron
B. The disintegration energy is shared between positron and neutrino in varying proportions
C. Neutrino is massless and carries no energy
D. Neutrino possesses very high kinetic energy

Answer

To solve the question regarding why beta particles (positrons) are emitted with different kinetic energies, we can break down the reasoning step by step.

### Step-by-Step Solution

1. **Understanding Beta Decay**:
- Beta decay involves the transformation of a neutron into a proton (or vice versa) within a nucleus, resulting in the emission of a beta particle (electron or positron) and a neutrino.
- The general representation of beta decay can be written as:
\[ _Z^AX \rightarrow _{Z+1}^AY + e^- + \bar{\nu} \]
- Here, \( e^- \) represents the emitted beta particle (electron), and \( \bar{\nu} \) represents the neutrino.

2. **Energy Distribution**:
- In beta decay, the total energy released (denoted as Q) is shared between the emitted beta particle and the neutrino.
- The energy distribution is not fixed; instead, it varies because both the beta particle and the neutrino can take different amounts of energy.

3. **Role of the Neutrino**:
- Wolfgang Pauli proposed the existence of neutrinos to account for the missing energy in beta decay.
- The neutrino is a nearly massless particle that carries away a portion of the energy released during the decay process.

4. **Variable Energy of Beta Particles**:
- The kinetic energy of the emitted beta particles varies because the energy Q is divided between the beta particle and the neutrino in varying proportions.
- This means that while the total energy is constant, the specific amount of energy that each particle receives can change, leading to a spectrum of kinetic energies for the emitted beta particles.

5. **Conclusion**:
- The reason beta particles are emitted with different kinetic energies is that the energy released during beta decay is shared between the positron and the neutrino in varying proportions.

### Final Answer
The beta particles (positrons) are emitted with different kinetic energies because the energy released during beta decay is shared between the positron and a neutrino in varying proportions.