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If uncertainty principle is applied to an object of mass 1 milligram, the uncertainty value of velocity and position will be
- a)0.2 x 10-4 m2 s-1
- b)0.52 x 106 m2 s-1
- c)0.52 x 10-28 m2 s-1
- d)2 x 10-34 m2 s-1
Correct answer is option 'C'. Can you explain this answer?
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If uncertainty principle is applied to an object of mass 1 milligram, ...
= 0.52 x 10-28 m2 s-1 (1 mg = 10-6 kg)
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If uncertainty principle is applied to an object of mass 1 milligram, ...
Explanation:
The uncertainty principle, also known as Heisenberg's uncertainty principle, states that it is impossible to simultaneously determine both the position and momentum (or velocity) of a particle with absolute certainty. The more accurately we try to measure one of these quantities, the less accurately we can know the other.
Given:
Mass of the object = 1 milligram = 1 x 10^(-6) kg
Formula:
The uncertainty principle is given by the formula:
Δx * Δp ≥ h/4π
where Δx is the uncertainty in position, Δp is the uncertainty in momentum, and h is the Planck's constant (h = 6.626 x 10^(-34) J s).
Calculating the uncertainty in momentum:
Since momentum is given by the product of mass and velocity (p = mv), we can write the uncertainty in momentum as:
Δp = m * Δv
where Δv is the uncertainty in velocity.
Calculating the uncertainty in position:
The uncertainty in position can be calculated using the formula:
Δx = h/4πΔp
Substituting the given values:
Δp = (1 x 10^(-6) kg) * Δv
Δx = (6.626 x 10^(-34) J s) / (4π * (1 x 10^(-6) kg) * Δv)
Simplifying the equation:
Δx * Δp = (6.626 x 10^(-34) J s) / (4π * (1 x 10^(-6) kg) * Δv) * (1 x 10^(-6) kg) * Δv
Δx * Δp = (6.626 x 10^(-34) J s) / (4π)
Δx * Δp = 5.27 x 10^(-35) J s
Converting the units:
1 J = 1 kg m^2/s^2
Δx * Δp = 5.27 x 10^(-35) kg m^2/s^2
Final answer:
The uncertainty value of velocity and position for an object of mass 1 milligram is 5.27 x 10^(-35) kg m^2/s^2. Therefore, the correct answer is option C: 0.52 x 10^(-28) m^2 s^(-1).
The uncertainty principle, also known as Heisenberg's uncertainty principle, states that it is impossible to simultaneously determine both the position and momentum (or velocity) of a particle with absolute certainty. The more accurately we try to measure one of these quantities, the less accurately we can know the other.
Given:
Mass of the object = 1 milligram = 1 x 10^(-6) kg
Formula:
The uncertainty principle is given by the formula:
Δx * Δp ≥ h/4π
where Δx is the uncertainty in position, Δp is the uncertainty in momentum, and h is the Planck's constant (h = 6.626 x 10^(-34) J s).
Calculating the uncertainty in momentum:
Since momentum is given by the product of mass and velocity (p = mv), we can write the uncertainty in momentum as:
Δp = m * Δv
where Δv is the uncertainty in velocity.
Calculating the uncertainty in position:
The uncertainty in position can be calculated using the formula:
Δx = h/4πΔp
Substituting the given values:
Δp = (1 x 10^(-6) kg) * Δv
Δx = (6.626 x 10^(-34) J s) / (4π * (1 x 10^(-6) kg) * Δv)
Simplifying the equation:
Δx * Δp = (6.626 x 10^(-34) J s) / (4π * (1 x 10^(-6) kg) * Δv) * (1 x 10^(-6) kg) * Δv
Δx * Δp = (6.626 x 10^(-34) J s) / (4π)
Δx * Δp = 5.27 x 10^(-35) J s
Converting the units:
1 J = 1 kg m^2/s^2
Δx * Δp = 5.27 x 10^(-35) kg m^2/s^2
Final answer:
The uncertainty value of velocity and position for an object of mass 1 milligram is 5.27 x 10^(-35) kg m^2/s^2. Therefore, the correct answer is option C: 0.52 x 10^(-28) m^2 s^(-1).
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If uncertainty principle is applied to an object of mass 1 milligram, the uncertainty value of velocity and position will bea)0.2 x 10-4 m2 s-1b)0.52 x 106 m2 s-1c)0.52 x 10-28 m2 s-1d)2 x 10-34 m2 s-1Correct answer is option 'C'. Can you explain this answer?
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If uncertainty principle is applied to an object of mass 1 milligram, the uncertainty value of velocity and position will bea)0.2 x 10-4 m2 s-1b)0.52 x 106 m2 s-1c)0.52 x 10-28 m2 s-1d)2 x 10-34 m2 s-1Correct answer is option 'C'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about If uncertainty principle is applied to an object of mass 1 milligram, the uncertainty value of velocity and position will bea)0.2 x 10-4 m2 s-1b)0.52 x 106 m2 s-1c)0.52 x 10-28 m2 s-1d)2 x 10-34 m2 s-1Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If uncertainty principle is applied to an object of mass 1 milligram, the uncertainty value of velocity and position will bea)0.2 x 10-4 m2 s-1b)0.52 x 106 m2 s-1c)0.52 x 10-28 m2 s-1d)2 x 10-34 m2 s-1Correct answer is option 'C'. Can you explain this answer?.
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