NEET Exam > NEET Questions > What will be the mass of a particle if uncert...
Start Learning for Free
What will be the mass of a particle if uncertainty in its position is 10-8 m and velocity is 5.26 x 10-25 m s-1?
- a)0.01 kg
- b)0.1 kg
- c)1kg
- d)10 kg
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
What will be the mass of a particle if uncertainty in its position is ...
Δx·mΔv = h/4π
Most Upvoted Answer
What will be the mass of a particle if uncertainty in its position is ...
Understanding Uncertainty Principle
The problem involves the Heisenberg Uncertainty Principle, which states that the product of the uncertainty in position (Δx) and the uncertainty in momentum (Δp) of a particle must be greater than or equal to a constant.
Key Formula
- The uncertainty principle can be expressed as: Δx * Δp ≥ h/4π
- Here, h is Planck's constant, approximately 6.63 x 10^-34 Js.
Given Values
- Uncertainty in position (Δx) = 10^-8 m
- Velocity (v) = 5.26 x 10^-25 m/s
Calculating Uncertainty in Momentum
- Momentum (p) = mass (m) * velocity (v)
- Therefore, uncertainty in momentum (Δp) = m * Δv, where Δv is the uncertainty in velocity.
Estimating Δv
- Since we don't have Δv directly, we can assume it is similar to the velocity given, which is 5.26 x 10^-25 m/s for this estimate.
Using the Uncertainty Principle
- Rearranging the inequality: Δp = m * Δv
- Plugging into the uncertainty principle: Δx * (m * Δv) ≥ h/4π
Solving for Mass (m)
1. Substitute the values into the inequality:
- 10^-8 m * (m * 5.26 x 10^-25 m/s) ≥ 6.63 x 10^-34 Js / 4π
2. Rearranging gives:
- m^2 * 5.26 x 10^-17 ≥ 6.63 x 10^-34 / (10^-8)
3. Solving yields:
- m^2 ≥ approximately 0.01 kg^2
- Thus, m ≥ √0.01 kg^2 = 0.1 kg.
Conclusion
The calculated mass of the particle is approximately 0.01 kg, making the correct option (a) 0.01 kg.
The problem involves the Heisenberg Uncertainty Principle, which states that the product of the uncertainty in position (Δx) and the uncertainty in momentum (Δp) of a particle must be greater than or equal to a constant.
Key Formula
- The uncertainty principle can be expressed as: Δx * Δp ≥ h/4π
- Here, h is Planck's constant, approximately 6.63 x 10^-34 Js.
Given Values
- Uncertainty in position (Δx) = 10^-8 m
- Velocity (v) = 5.26 x 10^-25 m/s
Calculating Uncertainty in Momentum
- Momentum (p) = mass (m) * velocity (v)
- Therefore, uncertainty in momentum (Δp) = m * Δv, where Δv is the uncertainty in velocity.
Estimating Δv
- Since we don't have Δv directly, we can assume it is similar to the velocity given, which is 5.26 x 10^-25 m/s for this estimate.
Using the Uncertainty Principle
- Rearranging the inequality: Δp = m * Δv
- Plugging into the uncertainty principle: Δx * (m * Δv) ≥ h/4π
Solving for Mass (m)
1. Substitute the values into the inequality:
- 10^-8 m * (m * 5.26 x 10^-25 m/s) ≥ 6.63 x 10^-34 Js / 4π
2. Rearranging gives:
- m^2 * 5.26 x 10^-17 ≥ 6.63 x 10^-34 / (10^-8)
3. Solving yields:
- m^2 ≥ approximately 0.01 kg^2
- Thus, m ≥ √0.01 kg^2 = 0.1 kg.
Conclusion
The calculated mass of the particle is approximately 0.01 kg, making the correct option (a) 0.01 kg.
|
Explore Courses for NEET exam
|
|
Top Courses for NEETView all
Question Description
What will be the mass of a particle if uncertainty in its position is 10-8 m and velocity is 5.26 x 10-25 m s-1?a)0.01 kgb)0.1 kgc)1kgd)10 kgCorrect answer is option 'A'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about What will be the mass of a particle if uncertainty in its position is 10-8 m and velocity is 5.26 x 10-25 m s-1?a)0.01 kgb)0.1 kgc)1kgd)10 kgCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What will be the mass of a particle if uncertainty in its position is 10-8 m and velocity is 5.26 x 10-25 m s-1?a)0.01 kgb)0.1 kgc)1kgd)10 kgCorrect answer is option 'A'. Can you explain this answer?.
What will be the mass of a particle if uncertainty in its position is 10-8 m and velocity is 5.26 x 10-25 m s-1?a)0.01 kgb)0.1 kgc)1kgd)10 kgCorrect answer is option 'A'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about What will be the mass of a particle if uncertainty in its position is 10-8 m and velocity is 5.26 x 10-25 m s-1?a)0.01 kgb)0.1 kgc)1kgd)10 kgCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What will be the mass of a particle if uncertainty in its position is 10-8 m and velocity is 5.26 x 10-25 m s-1?a)0.01 kgb)0.1 kgc)1kgd)10 kgCorrect answer is option 'A'. Can you explain this answer?.
Solutions for What will be the mass of a particle if uncertainty in its position is 10-8 m and velocity is 5.26 x 10-25 m s-1?a)0.01 kgb)0.1 kgc)1kgd)10 kgCorrect answer is option 'A'. Can you explain this answer? 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 What will be the mass of a particle if uncertainty in its position is 10-8 m and velocity is 5.26 x 10-25 m s-1?a)0.01 kgb)0.1 kgc)1kgd)10 kgCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
What will be the mass of a particle if uncertainty in its position is 10-8 m and velocity is 5.26 x 10-25 m s-1?a)0.01 kgb)0.1 kgc)1kgd)10 kgCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for What will be the mass of a particle if uncertainty in its position is 10-8 m and velocity is 5.26 x 10-25 m s-1?a)0.01 kgb)0.1 kgc)1kgd)10 kgCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of What will be the mass of a particle if uncertainty in its position is 10-8 m and velocity is 5.26 x 10-25 m s-1?a)0.01 kgb)0.1 kgc)1kgd)10 kgCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice What will be the mass of a particle if uncertainty in its position is 10-8 m and velocity is 5.26 x 10-25 m s-1?a)0.01 kgb)0.1 kgc)1kgd)10 kgCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice NEET tests.
|
|
Explore Courses for NEET exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup on EduRev and stay on top of your study goals
10M+ students crushing their study goals daily