NEET Exam  >  NEET Questions  >  A uranium-238 nucleus, initially at rest, emi... Start Learning for Free
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)?
Verified Answer
A uranium-238 nucleus, initially at rest, emits an alpha particle with...
Method to Solve :

This question is part of UPSC exam. View all NEET courses
Most Upvoted Answer
A uranium-238 nucleus, initially at rest, emits an alpha particle with...
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
Attention NEET Students!
To make sure you are not studying endlessly, EduRev has designed NEET study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in NEET.
Explore Courses for NEET exam

Similar NEET Doubts

Top Courses for NEET

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)?
Question Description
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)?.
Solutions 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)? in English & in Hindi are available as part of our courses for NEET. Download more important topics, notes, lectures and mock test series for NEET Exam by signing up for free.
Here you can find the meaning of 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)? defined & explained in the simplest way possible. Besides giving the explanation of 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 detailed solution 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)? has been provided alongside types of 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)? theory, EduRev gives you an ample number of questions to practice 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)? tests, examples and also practice NEET tests.
Explore Courses for NEET exam

Top Courses for NEET

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev