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The position of both, an electron and a helium atom is known within 1.0 mm. Further more the momentum of the electron is known within 5.0 x 10-26 kg ms-1. The minimum uncertainty in the measurement of the momentum of the helium atom is
- a)50.0 kg ms-1
- b)80.0 kg ms-1
- c)80.0 x 10-26 kg ms-1
- d)5.0 x 10-26 kg ms-1
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The position of both, an electron and a helium atom is known within 1....
Given,
Position of both an electron and a Helium atom = 1 nm
The momentum of an electron =
Uncertainty principle: It is defined as the position and the momentum both can not be determined simultaneously.
According to the Uncertainty principle,
h = Planck`s constant
When the position of an electron and helium atom is the same and the momentum of an electron is known then the momentum of the helium atom is equal to the momentum of an electron.
Therefore, the momentum of the Helium atom is 5.0 x 10-26 kg ms-1
Most Upvoted Answer
The position of both, an electron and a helium atom is known within 1....
Explanation:
Uncertainty Principle:
The uncertainty principle, formulated by Werner Heisenberg, states that it is impossible to simultaneously determine with perfect accuracy both the position and momentum of a particle. The more accurately we know the position of a particle, the less accurately we know its momentum, and vice versa. Mathematically, the uncertainty principle is expressed as:
Δx * Δp ≥ h/4π
where Δx represents the uncertainty in position, Δp represents the uncertainty in momentum, and h is the Planck's constant.
Given Information:
- Uncertainty in position of both the electron and helium atom = 1.0 mm = 1.0 x 10^-3 m
- Uncertainty in momentum of the electron = 5.0 x 10^-26 kg ms^-1
Finding the Minimum Uncertainty in Momentum of the Helium Atom:
To find the minimum uncertainty in the measurement of the momentum of the helium atom, we need to use the uncertainty principle equation.
Δx * Δp ≥ h/4π
Since the position uncertainty is the same for both the electron and helium atom, we can use the same value for Δx.
Δx = 1.0 x 10^-3 m
Plugging in the values, we get:
(1.0 x 10^-3 m) * Δp ≥ h/4π
To find the minimum uncertainty, we need to find the minimum value of Δp. Rearranging the equation, we get:
Δp ≥ h/(4π * Δx)
Plugging in the values of h and Δx, we get:
Δp ≥ (6.626 x 10^-34 J s)/(4π * 1.0 x 10^-3 m)
Simplifying the expression, we get:
Δp ≥ 5.28 x 10^-31 kg m s^-1
Therefore, the minimum uncertainty in the measurement of the momentum of the helium atom is 5.28 x 10^-31 kg m s^-1, which is closest to option 'D' (5.0 x 10^-26 kg m s^-1).
Uncertainty Principle:
The uncertainty principle, formulated by Werner Heisenberg, states that it is impossible to simultaneously determine with perfect accuracy both the position and momentum of a particle. The more accurately we know the position of a particle, the less accurately we know its momentum, and vice versa. Mathematically, the uncertainty principle is expressed as:
Δx * Δp ≥ h/4π
where Δx represents the uncertainty in position, Δp represents the uncertainty in momentum, and h is the Planck's constant.
Given Information:
- Uncertainty in position of both the electron and helium atom = 1.0 mm = 1.0 x 10^-3 m
- Uncertainty in momentum of the electron = 5.0 x 10^-26 kg ms^-1
Finding the Minimum Uncertainty in Momentum of the Helium Atom:
To find the minimum uncertainty in the measurement of the momentum of the helium atom, we need to use the uncertainty principle equation.
Δx * Δp ≥ h/4π
Since the position uncertainty is the same for both the electron and helium atom, we can use the same value for Δx.
Δx = 1.0 x 10^-3 m
Plugging in the values, we get:
(1.0 x 10^-3 m) * Δp ≥ h/4π
To find the minimum uncertainty, we need to find the minimum value of Δp. Rearranging the equation, we get:
Δp ≥ h/(4π * Δx)
Plugging in the values of h and Δx, we get:
Δp ≥ (6.626 x 10^-34 J s)/(4π * 1.0 x 10^-3 m)
Simplifying the expression, we get:
Δp ≥ 5.28 x 10^-31 kg m s^-1
Therefore, the minimum uncertainty in the measurement of the momentum of the helium atom is 5.28 x 10^-31 kg m s^-1, which is closest to option 'D' (5.0 x 10^-26 kg m s^-1).
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The position of both, an electron and a helium atom is known within 1....
I think we should use heinsbergs uncertainty principle
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The position of both, an electron and a helium atom is known within 1.0 mm. Further more the momentum of the electron is known within 5.0 x 10-26 kg ms-1. The minimum uncertainty in the measurement of the momentum of the helium atom isa)50.0 kg ms-1b)80.0 kg ms-1c)80.0 x 10-26 kg ms-1d)5.0 x 10-26 kg ms-1Correct answer is option 'D'. Can you explain this answer?
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The position of both, an electron and a helium atom is known within 1.0 mm. Further more the momentum of the electron is known within 5.0 x 10-26 kg ms-1. The minimum uncertainty in the measurement of the momentum of the helium atom isa)50.0 kg ms-1b)80.0 kg ms-1c)80.0 x 10-26 kg ms-1d)5.0 x 10-26 kg ms-1Correct answer is option 'D'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The position of both, an electron and a helium atom is known within 1.0 mm. Further more the momentum of the electron is known within 5.0 x 10-26 kg ms-1. The minimum uncertainty in the measurement of the momentum of the helium atom isa)50.0 kg ms-1b)80.0 kg ms-1c)80.0 x 10-26 kg ms-1d)5.0 x 10-26 kg ms-1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The position of both, an electron and a helium atom is known within 1.0 mm. Further more the momentum of the electron is known within 5.0 x 10-26 kg ms-1. The minimum uncertainty in the measurement of the momentum of the helium atom isa)50.0 kg ms-1b)80.0 kg ms-1c)80.0 x 10-26 kg ms-1d)5.0 x 10-26 kg ms-1Correct answer is option 'D'. Can you explain this answer?.
The position of both, an electron and a helium atom is known within 1.0 mm. Further more the momentum of the electron is known within 5.0 x 10-26 kg ms-1. The minimum uncertainty in the measurement of the momentum of the helium atom isa)50.0 kg ms-1b)80.0 kg ms-1c)80.0 x 10-26 kg ms-1d)5.0 x 10-26 kg ms-1Correct answer is option 'D'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The position of both, an electron and a helium atom is known within 1.0 mm. Further more the momentum of the electron is known within 5.0 x 10-26 kg ms-1. The minimum uncertainty in the measurement of the momentum of the helium atom isa)50.0 kg ms-1b)80.0 kg ms-1c)80.0 x 10-26 kg ms-1d)5.0 x 10-26 kg ms-1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The position of both, an electron and a helium atom is known within 1.0 mm. Further more the momentum of the electron is known within 5.0 x 10-26 kg ms-1. The minimum uncertainty in the measurement of the momentum of the helium atom isa)50.0 kg ms-1b)80.0 kg ms-1c)80.0 x 10-26 kg ms-1d)5.0 x 10-26 kg ms-1Correct answer is option 'D'. Can you explain this answer?.
Solutions for The position of both, an electron and a helium atom is known within 1.0 mm. Further more the momentum of the electron is known within 5.0 x 10-26 kg ms-1. The minimum uncertainty in the measurement of the momentum of the helium atom isa)50.0 kg ms-1b)80.0 kg ms-1c)80.0 x 10-26 kg ms-1d)5.0 x 10-26 kg ms-1Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 11.
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