Two beta-minus particles, each with 75 keV of kinetic energy, undergo Bremsstrahlung interactions. One beta-minus particle has 35 kev after the interaction, and the other has 61 keV after the interaction. What is the Bremsstrahlung x-ray energy in each case? Which of the two beta-minus particles came closest to the nucleus?

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**Problem Description:**

Two beta-minus particles, each with 75 keV of kinetic energy, undergo Bremsstrahlung interactions. One beta-minus particle has 35 keV after the interaction, and the other has 61 keV after the interaction. What is the Bremsstrahlung X-ray energy in each case? Which of the two beta-minus particles came closest to the nucleus?

**Solution Explanation:**

Bremsstrahlung interaction involves the emission of X-rays due to the deceleration of beta particles when they come close to atomic nuclei. The difference in kinetic energy before and after the interaction determines the X-ray energy emitted.

1. **First Beta-minus Particle:**
   - Initial Kinetic Energy: 75 keV
   - Final Kinetic Energy: 35 keV
   - Bremsstrahlung X-ray Energy = Initial Kinetic Energy - Final Kinetic Energy = 75 keV - 35 keV = 40 keV

2. **Second Beta-minus Particle:**
   - Initial Kinetic Energy: 75 keV
   - Final Kinetic Energy: 61 keV
   - Bremsstrahlung X-ray Energy = Initial Kinetic Energy - Final Kinetic Energy = 75 keV - 61 keV = 14 keV

**Conclusion:**

The first beta-minus particle, which had a higher Bremsstrahlung X-ray energy of 40 keV, came closest to the nucleus as it lost more kinetic energy compared to the second particle.
Transcribed Image Text:**Problem Description:** Two beta-minus particles, each with 75 keV of kinetic energy, undergo Bremsstrahlung interactions. One beta-minus particle has 35 keV after the interaction, and the other has 61 keV after the interaction. What is the Bremsstrahlung X-ray energy in each case? Which of the two beta-minus particles came closest to the nucleus? **Solution Explanation:** Bremsstrahlung interaction involves the emission of X-rays due to the deceleration of beta particles when they come close to atomic nuclei. The difference in kinetic energy before and after the interaction determines the X-ray energy emitted. 1. **First Beta-minus Particle:** - Initial Kinetic Energy: 75 keV - Final Kinetic Energy: 35 keV - Bremsstrahlung X-ray Energy = Initial Kinetic Energy - Final Kinetic Energy = 75 keV - 35 keV = 40 keV 2. **Second Beta-minus Particle:** - Initial Kinetic Energy: 75 keV - Final Kinetic Energy: 61 keV - Bremsstrahlung X-ray Energy = Initial Kinetic Energy - Final Kinetic Energy = 75 keV - 61 keV = 14 keV **Conclusion:** The first beta-minus particle, which had a higher Bremsstrahlung X-ray energy of 40 keV, came closest to the nucleus as it lost more kinetic energy compared to the second particle.
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Solution:

Two beta minus particles undergo bremsstrahlung interaction. Each particle has an incident energy of 75 keV. The beta minus particle will be deflected towards the positive charge nucleus. Due to the deflection of the incident particle the acceleration or acceleration occurs depending on the particle's energy. Accelerelareted particles radiate energy. The energy difference between the incident radiation and the outgoing radiation is the energy of the bremsstrahlung x-ray energy. For the first particle:

Ei=75 keV E0=35 keVX-ray energy is:Ex=Ei-E0     =75-35 keV     =40 keV

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