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Passage II
The position and momentum of electron of energy 0.5 keV are simultaneously determined. Its position is located within 0.2 nm
Q. Percentage uncertainty in momentum is
  • a)
    2.2%
  • b)
    0.022
  • c)
    1.1%
  • d)
    0.011%
Correct answer is option 'A'. Can you explain this answer?
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Passage IIThe position and momentum of electron of energy 0.5 keV are ...




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Passage IIThe position and momentum of electron of energy 0.5 keV are ...
Given information:
- Energy of electron = 0.5 keV
- Position of electron is located within 0.2 nm
- We need to find the percentage uncertainty in momentum

Formulae used:
- De Broglie wavelength (λ) = h/p, where h is Planck's constant and p is momentum
- Uncertainty principle (Δx * Δp >= h/4π), where Δx is uncertainty in position and Δp is uncertainty in momentum

Calculation:
- Energy of electron = (1/2)mv^2 = (1/2)(9.1 x 10^-31 kg)(v^2) = 0.5 keV
- Solving for v, we get v = 1.79 x 10^6 m/s
- Using the formula λ = h/p, we can find the De Broglie wavelength of the electron
- λ = h/p = h/(mv) = (6.626 x 10^-34 J s)/(9.1 x 10^-31 kg)(1.79 x 10^6 m/s) = 1.23 x 10^-10 m
- Since the position of the electron is located within 0.2 nm (i.e. 2 x 10^-10 m), we can assume the uncertainty in position to be Δx = 0.2 nm
- Using the uncertainty principle, we can find the uncertainty in momentum
- Δx * Δp >= h/4π
- Δp >= h/(4πΔx)
- Δp >= (6.626 x 10^-34 J s)/(4π(0.2 x 10^-9 m))
- Δp >= 0.263 x 10^-24 kg m/s
- Percentage uncertainty in momentum = (Δp/p) x 100%
- Percentage uncertainty in momentum = [(0.263 x 10^-24 kg m/s)/(9.1 x 10^-31 kg)(1.79 x 10^6 m/s)] x 100%
- Percentage uncertainty in momentum = 2.2%

Therefore, the correct answer is option A (2.2%).
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Can you explain the answer of this question below:The French physicist Louis de-Broglie in 1924 postulated that matter, like radiation, should exhibit a dual behaviour. He proposed the following relationship between the wavelength of a material particle, its linear momentum p and planck constant h.The de Broglie relation implies that the wavelength of a particle should decreases as its velocity increases. It also implies that for a given velocity heavier particles should have shorter wavelength than lighter particles. The waves associated with particles in motion are called matter waves or de Broglie waves.These waves differ from the electromagnetic waves as they,(i) have lower velocities(ii) have no electrical and magnetic fields and(iii) are not emitted by the particle under consideration.The experimental confirmation of the deBroglie relation was obtained when Davisson and Germer, in 1927, observed that a beam of electrons is diffracted by a nickel crystal. As diffraction is a characteristic property of waves, hence the beam of electron behaves as a wave, as proposed by deBroglie.Werner Heisenberg considered the limits of how precisely we can measure properties of an electron or other microscopic particle like electron. He determined that there is a fundamental limit of how closely we can measure both position and momentum. The more accurately we measure the momentum of a particle, the less accurately we can determine its position. The converse is also ture. This is summed up in what we now call the Heisenberg uncertainty principle : It is impossible to determine simultaneously and precisely both the momentum and position of a particle. The product of undertainty in the position, x and the uncertainity in the momentum (mv) must be greater than or equal to h/4. i.e.Q.The correct order of wavelength of Hydrogen (1H1), Deuterium (1H2) and Tritium (1H3) moving with same kinetic energy is :A:H D TB:H = D = TC:H D TD:H D TThe answer is a.

The French physicist Louis de-Broglie in 1924 postulated that matter, like radiation, should exhibit a dual behaviour. He proposed the following relationship between the wavelength of a material particle, its linear momentum p and planck constant h.The de Broglie relation implies that the wavelength of a particle should decreases as its velocity increases. It also implies that for a given velocity heavier particles should have shorter wavelength than lighter particles. The waves associated with particles in motion are called matter waves or de Broglie waves.These waves differ from the electromagnetic waves as they,(i) have lower velocities(ii) have no electrical and magnetic fields and(iii) are not emitted by the particle under consideration.The experimental confirmation of the deBroglie relation was obtained when Davisson and Germer, in 1927, observed that a beam of electrons is diffracted by a nickel crystal. As diffraction is a characteristic property of waves, hence the beam of electron behaves as a wave, as proposed by deBroglie.Werner Heisenberg considered the limits of how precisely we can measure properties of an electron or other microscopic particle like electron. He determined that there is a fundamental limit of how closely we can measure both position and momentum. The more accurately we measure the momentum of a particle, the less accurately we can determine its position. The converse is also ture. This is summed up in what we now call the Heisenberg uncertainty principle : It is impossible to determine simultaneously and precisely both the momentum and position of a particle. The product of undertainty in the position, x and the uncertainity in the momentum (mv) must be greater than or equal to h/4. i.e.Q. The transition, so that the de - Broglie wavelength of electron becomes 3 times of its initial value in He+ ion will be

The French physicist Louis de-Broglie in 1924 postulated that matter, like radiation, should exhibit a dual behaviour. He proposed the following relationship between the wavelength of a material particle, its linear momentum p and planck constant h.The de Broglie relation implies that the wavelength of a particle should decreases as its velocity increases. It also implies that for a given velocity heavier particles should have shorter wavelength than lighter particles. The waves associated with particles in motion are called matter waves or de Broglie waves.These waves differ from the electromagnetic waves as they,(i) have lower velocities(ii) have no electrical and magnetic fields and(iii) are not emitted by the particle under consideration.The experimental confirmation of the deBroglie relation was obtained when Davisson and Germer, in 1927, observed that a beam of electrons is diffracted by a nickel crystal. As diffraction is a characteristic property of waves, hence the beam of electron behaves as a wave, as proposed by deBroglie.Werner Heisenberg considered the limits of how precisely we can measure properties of an electron or other microscopic particle like electron. He determined that there is a fundamental limit of how closely we can measure both position and momentum. The more accurately we measure the momentum of a particle, the less accurately we can determine its position. The converse is also ture. This is summed up in what we now call the Heisenberg uncertainty principle : It is impossible to determine simultaneously and precisely both the momentum and position of a particle. The product of undertainty in the position, x and the uncertainity in the momentum (mv) must be greater than or equal to h/4. i.e.Q. If the uncertainty in velocity position is same, then the uncertainty in momentum will be

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Passage IIThe position and momentum of electron of energy 0.5 keV are simultaneously determined. Its position is located within 0.2 nmQ.Percentage uncertainty in momentum isa)2.2%b)0.022c)1.1%d)0.011%Correct answer is option 'A'. Can you explain this answer?
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Passage IIThe position and momentum of electron of energy 0.5 keV are simultaneously determined. Its position is located within 0.2 nmQ.Percentage uncertainty in momentum isa)2.2%b)0.022c)1.1%d)0.011%Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Passage IIThe position and momentum of electron of energy 0.5 keV are simultaneously determined. Its position is located within 0.2 nmQ.Percentage uncertainty in momentum isa)2.2%b)0.022c)1.1%d)0.011%Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Passage IIThe position and momentum of electron of energy 0.5 keV are simultaneously determined. Its position is located within 0.2 nmQ.Percentage uncertainty in momentum isa)2.2%b)0.022c)1.1%d)0.011%Correct answer is option 'A'. Can you explain this answer?.
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