During `beta`-decay of stationary nucleus , an electron is observed with a kinetic energy 1.0 MeV . From this ,what can be concluded about the Q-value of the decay ?

Options

A. Q=1.0 MeV
B. `Q le 1.0 MeV`
C. `Q ge 1.0 MeV`
D. Noting can be concluded about the Q-value

Answer

To solve the problem regarding the Q-value of the beta decay given that an electron is observed with a kinetic energy of 1.0 MeV, we can follow these steps:

### Step 1: Understand the Beta Decay Process
In beta decay, a parent nucleus transforms into a daughter nucleus by emitting an electron (beta particle) and an antineutrino. The general reaction can be represented as:
\[ X \rightarrow Y + e^- + \bar{\nu} \]
where \(X\) is the parent nucleus, \(Y\) is the daughter nucleus, \(e^-\) is the emitted electron, and \(\bar{\nu}\) is the antineutrino.

### Step 2: Analyze the Energy Conservation
In the decay process, the total energy before the decay (when the parent nucleus is at rest) is equal to the total energy after the decay. Initially, the kinetic energy of the parent nucleus is zero. After the decay, the kinetic energy of the emitted electron is given as 1.0 MeV.

### Step 3: Relate Kinetic Energy to Q-value
The Q-value of a nuclear reaction is defined as the total energy released during the decay. It can be expressed in terms of the mass-energy equivalence as:
\[ Q = \Delta m c^2 \]
where \(\Delta m\) is the mass difference between the parent and daughter nuclei and \(c\) is the speed of light.

### Step 4: Determine the Implications of the Kinetic Energy
Since the electron has a kinetic energy of 1.0 MeV, this energy is a part of the total energy released in the decay. However, there are also other forms of energy released, such as the kinetic energy of the daughter nucleus and the antineutrino. Therefore, the total energy released (Q-value) must be greater than the kinetic energy of the emitted electron.

### Step 5: Conclusion about the Q-value
From the above analysis, we can conclude that:
\[ Q > 1.0 \text{ MeV} \]
Thus, the Q-value of the decay must be greater than 1.0 MeV.

### Final Answer
The Q-value of the beta decay is greater than 1.0 MeV.

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