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The energy spectrum of beta - particle [...

The energy spectrum of `beta` - particle [number `N(E)` as a function of `beta` - energy E] emitted from a radioactive source is

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To solve the problem regarding the energy spectrum of beta particles emitted from a radioactive source, we need to analyze the behavior of the number of emitted beta particles (N(E)) as a function of their energy (E). The question provides us with four options in the form of graphs, and we need to determine which graph correctly represents this relationship. ### Step-by-Step Solution: 1. **Understanding Beta Particle Emission**: - Beta particles are emitted during radioactive decay and have a continuous energy spectrum ranging from 0 to a maximum energy (E_max). The number of beta particles emitted at a specific energy level (N(E)) varies with energy. 2. **Analyzing the Energy Spectrum**: - At very low energies (E ≈ 0), the number of emitted beta particles (N(E)) is expected to be at its maximum because there are many particles with low energy. - As the energy increases towards the maximum energy (E_max), the number of emitted beta particles decreases. This is due to the nature of the decay process and the distribution of energy among the emitted particles. 3. **Identifying the Correct Graph**: - We need to find a graph that starts at a high value of N(E) when E is 0 and decreases as E approaches E_max. - The correct graph should reflect this behavior: high N(E) at low E, tapering off to low N(E) as E approaches E_max. 4. **Evaluating the Options**: - **Option 1**: Starts high at E = 0 and decreases as E increases. This matches our expectations. - **Option 2**: Shows an increase in N(E) as E increases, which is incorrect. - **Option 3**: Shows a constant value and then a decrease, which does not fit the expected behavior. - **Option 4**: Similar to option 3, starts high but does not show the correct decrease pattern. 5. **Conclusion**: - Based on the analysis, **Option 1** is the correct representation of the energy spectrum of beta particles emitted from a radioactive source. ### Final Answer: The correct option is **Option 1**.
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