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A uranium-238 nucleus, initially at rest, emits an alpha particle with energy E. The recoil speed of residual nucleus thorium-234 is ( masses are same as their mass number)?
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A uranium-238 nucleus, initially at rest, emits an alpha particle with...
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Introduction
When a uranium-238 nucleus emits an alpha particle, it undergoes radioactive decay and transforms into a thorium-234 nucleus. This process is spontaneous and occurs due to the instability of the uranium-238 nucleus. In this response, we will explore the recoil speed of the residual nucleus thorium-234 after the emission of the alpha particle.
Conservation of Momentum
The recoil speed of the residual nucleus can be determined by considering the conservation of momentum. According to the law of conservation of momentum, the total momentum of an isolated system remains constant if no external forces act on it. In this case, the system consists of the uranium-238 nucleus, the alpha particle, and the thorium-234 nucleus.
Initial Momentum
Initially, the uranium-238 nucleus is at rest, so its momentum is zero. The alpha particle, on the other hand, possesses momentum due to its energy E. The momentum of the alpha particle is given by the product of its mass and velocity:
Momentum of alpha particle = mass of alpha particle × velocity of alpha particle
Since the masses are the same as their mass numbers, the mass of the alpha particle is 4 atomic mass units (amu).
Final Momentum
After the emission of the alpha particle, the uranium-238 nucleus is transformed into the thorium-234 nucleus. The thorium-234 nucleus recoils in the opposite direction to conserve momentum. The momentum of the thorium-234 nucleus can be calculated using the same formula as before:
Momentum of thorium-234 nucleus = mass of thorium-234 nucleus × velocity of thorium-234 nucleus
The mass of the thorium-234 nucleus is 234 atomic mass units (amu).
Conservation of Momentum Equation
Applying the law of conservation of momentum, we can write the equation:
Momentum of alpha particle = Momentum of thorium-234 nucleus
Mass of alpha particle × velocity of alpha particle = Mass of thorium-234 nucleus × velocity of thorium-234 nucleus
Calculation of Recoil Speed
To determine the recoil speed of the thorium-234 nucleus, we rearrange the equation:
Velocity of thorium-234 nucleus = (Mass of alpha particle / Mass of thorium-234 nucleus) × velocity of alpha particle
Since the masses are the same as their mass numbers, the mass of the alpha particle is 4 atomic mass units (amu) and the mass of the thorium-234 nucleus is 234 atomic mass units (amu).
Velocity of thorium-234 nucleus = (4 amu / 234 amu) × velocity of alpha particle
Simplifying the equation:
Velocity of thorium-234 nucleus = (2 / 117) × velocity of alpha particle
Therefore, the recoil speed of the residual nucleus thorium-234 is given by the equation above.
Conclusion
When a uranium-238 nucleus emits an alpha particle with energy E, the recoil speed of the residual nucleus thorium-234 can be calculated using the conservation of momentum. By considering the masses of the particles involved
When a uranium-238 nucleus emits an alpha particle, it undergoes radioactive decay and transforms into a thorium-234 nucleus. This process is spontaneous and occurs due to the instability of the uranium-238 nucleus. In this response, we will explore the recoil speed of the residual nucleus thorium-234 after the emission of the alpha particle.
Conservation of Momentum
The recoil speed of the residual nucleus can be determined by considering the conservation of momentum. According to the law of conservation of momentum, the total momentum of an isolated system remains constant if no external forces act on it. In this case, the system consists of the uranium-238 nucleus, the alpha particle, and the thorium-234 nucleus.
Initial Momentum
Initially, the uranium-238 nucleus is at rest, so its momentum is zero. The alpha particle, on the other hand, possesses momentum due to its energy E. The momentum of the alpha particle is given by the product of its mass and velocity:
Momentum of alpha particle = mass of alpha particle × velocity of alpha particle
Since the masses are the same as their mass numbers, the mass of the alpha particle is 4 atomic mass units (amu).
Final Momentum
After the emission of the alpha particle, the uranium-238 nucleus is transformed into the thorium-234 nucleus. The thorium-234 nucleus recoils in the opposite direction to conserve momentum. The momentum of the thorium-234 nucleus can be calculated using the same formula as before:
Momentum of thorium-234 nucleus = mass of thorium-234 nucleus × velocity of thorium-234 nucleus
The mass of the thorium-234 nucleus is 234 atomic mass units (amu).
Conservation of Momentum Equation
Applying the law of conservation of momentum, we can write the equation:
Momentum of alpha particle = Momentum of thorium-234 nucleus
Mass of alpha particle × velocity of alpha particle = Mass of thorium-234 nucleus × velocity of thorium-234 nucleus
Calculation of Recoil Speed
To determine the recoil speed of the thorium-234 nucleus, we rearrange the equation:
Velocity of thorium-234 nucleus = (Mass of alpha particle / Mass of thorium-234 nucleus) × velocity of alpha particle
Since the masses are the same as their mass numbers, the mass of the alpha particle is 4 atomic mass units (amu) and the mass of the thorium-234 nucleus is 234 atomic mass units (amu).
Velocity of thorium-234 nucleus = (4 amu / 234 amu) × velocity of alpha particle
Simplifying the equation:
Velocity of thorium-234 nucleus = (2 / 117) × velocity of alpha particle
Therefore, the recoil speed of the residual nucleus thorium-234 is given by the equation above.
Conclusion
When a uranium-238 nucleus emits an alpha particle with energy E, the recoil speed of the residual nucleus thorium-234 can be calculated using the conservation of momentum. By considering the masses of the particles involved
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A uranium-238 nucleus, initially at rest, emits an alpha particle with energy E. The recoil speed of residual nucleus thorium-234 is ( masses are same as their mass number)?
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A uranium-238 nucleus, initially at rest, emits an alpha particle with energy E. The recoil speed of residual nucleus thorium-234 is ( masses are same as their mass number)? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A uranium-238 nucleus, initially at rest, emits an alpha particle with energy E. The recoil speed of residual nucleus thorium-234 is ( masses are same as their mass number)? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A uranium-238 nucleus, initially at rest, emits an alpha particle with energy E. The recoil speed of residual nucleus thorium-234 is ( masses are same as their mass number)?.
A uranium-238 nucleus, initially at rest, emits an alpha particle with energy E. The recoil speed of residual nucleus thorium-234 is ( masses are same as their mass number)? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A uranium-238 nucleus, initially at rest, emits an alpha particle with energy E. The recoil speed of residual nucleus thorium-234 is ( masses are same as their mass number)? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A uranium-238 nucleus, initially at rest, emits an alpha particle with energy E. The recoil speed of residual nucleus thorium-234 is ( masses are same as their mass number)?.
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