In mathematical terms, Heisenberg's principle states that the uncertainty in the electron's position, `Deltax`, times the uncertainty in its momentum, `Deltapx`, is_____the quantity `h//4pi`.
(i) equal to (ii) less than
(iii) greater than
In mathematical terms, Heisenberg's principle states that the uncertainty in the electron's position, `Deltax`, times the uncertainty in its momentum, `Deltapx`, is_____the quantity `h//4pi`.
(i) equal to (ii) less than
(iii) greater than
(i) equal to (ii) less than
(iii) greater than
A
`(i)`or`(ii)`
B
`(i)`or`(iii)`
C
`(i)`
D
`(iii)`
Text Solution
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The correct Answer is:
B
`DeltaxDeltap_(x) ge (h)/(4pi)`
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Assume that we are travelling at a speed of 90 km h^(-1) in a small car with a mass of 1250 kg . If the unceratinty in the velocity of the car is 1%(Deltav = 0.9 km h^(-1)) , what is the uncertainty (in metars) in the position of the car? Strategy: Heisenberg's uncertainty relasionship states that the uncertainity in an object's position, Deltax , times the uncertainty in its momentum, Deltap_(x) , is equal to or greater than the quantity h//pi4 . In the present case, we need to find Deltax when Deltav is known. We need to convert Deltav into ms^(-1) ).
The mass m of an electron is 9.1 xx 10^(31)kg and the velocity v of an electron in the first Bohr orbit of a hydrogen atom is 2.2 xx 10^(6)ms^(-1) . Assuming that the velocity is known within 10% (Deltav = 0.22 xx 10^(6)ms^(-1)) , calculate the uncertainty in the electron's position in a hydrogen atom. Strategy: According to Heisenberg's principle, the uncertainty in the postion (Deltax) of any moving particle multiplied by the uncertainity of momentum (Deltap_(x)) can never be less than h//4pi . In the given case, Delta v is known and we need to find Deltax .
Knowledge Check
The uncertainty in position of an electron in a certain state is 5 xx 10^(-10) m . The uncertainty in its momentum might be
The uncertainty in position of an electron in a certain state is 5 xx 10^(-10) m . The uncertainty in its momentum might be
A
`5.0 xx 10^(-24) kg.m//s`
B
`4.0 xx 10^(-24) kg.m//s`
C
`3.0 xx 10^(-24) kg.m//s`
D
All of the above
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 .lambda of a material particle,its linear momentum P and Planck constant h. lambda=(h)/(p)=(h)/(mv) The de Broglie relaion that the wavelength of a particle should decrease as its velocity increases. It also implies that for a given velocity heavier particles should have shorter wavelength than lighter particles.The 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 expermental confirmation of the de Broglie relation was obtained when Davission and Germer in 1927, observed. As diffraction is a characteristic property of waves, hence the beam of electrons behave as a wave as proposed by de Broglie. 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 can determine its position. The converse is also true. 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 uncertainty in the position, Deltax and the uncertainty in the momentum Delta(mv) must be greater than or equal to (h)/(4pi), i.e., Deltax Delta(mv)ge(h)/(4pi) If the uncertainty in velocity and posititon is same then the uncertainty in momentum 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 .lambda of a material particle,its linear momentum P and Planck constant h. lambda=(h)/(p)=(h)/(mv) The de Broglie relaion that the wavelength of a particle should decrease as its velocity increases. It also implies that for a given velocity heavier particles should have shorter wavelength than lighter particles.The 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 expermental confirmation of the de Broglie relation was obtained when Davission and Germer in 1927, observed. As diffraction is a characteristic property of waves, hence the beam of electrons behave as a wave as proposed by de Broglie. 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 can determine its position. The converse is also true. 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 uncertainty in the position, Deltax and the uncertainty in the momentum Delta(mv) must be greater than or equal to (h)/(4pi), i.e., Deltax Delta(mv)ge(h)/(4pi) If the uncertainty in velocity and posititon is same then the uncertainty in momentum will be :
A
`sqrt((hm)/(4pi))`
B
`m.sqrt((h)/(4pi))`
C
`sqrt((h)/(4pim))`
D
`1/msqrt((h)/(4pim))`
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 .lambda of a material particle,its linear momentum P and Planck constant h. lambda=(h)/(p)=(h)/(mv) The de Broglie relaion that the wavelength of a particle should decrease as its velocity increases. It also implies that for a given velocity heavier particles should have shorter wavelength than lighter particles.The 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 expermental confirmation of the de Broglie relation was obtained when Davission and Germer in 1927, observed. As diffraction is a characteristic property of waves, hence the beam of electrons behave as a wave as proposed by de Broglie. 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 can determine its position. The converse is also true. 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 uncertainty in the position, Deltax and the uncertainty in the momentum Delta(mv) must be greater than or equal to (h)/(4pi), i.e., Deltax Delta(mv)ge(h)/(4pi) 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 .lambda of a material particle,its linear momentum P and Planck constant h. lambda=(h)/(p)=(h)/(mv) The de Broglie relaion that the wavelength of a particle should decrease as its velocity increases. It also implies that for a given velocity heavier particles should have shorter wavelength than lighter particles.The 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 expermental confirmation of the de Broglie relation was obtained when Davission and Germer in 1927, observed. As diffraction is a characteristic property of waves, hence the beam of electrons behave as a wave as proposed by de Broglie. 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 can determine its position. The converse is also true. 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 uncertainty in the position, Deltax and the uncertainty in the momentum Delta(mv) must be greater than or equal to (h)/(4pi), i.e., Deltax Delta(mv)ge(h)/(4pi) The transition so that the de Broglie wavelength of electron becomes 3 times of its initial value in He^(+) ion will be :
A
`2 to 5`
B
`3 to 2`
C
`2 to 6`
D
`1 to 2`
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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 .lambda of a material particle,its linear momentum P and Planck constant h. lambda=(h)/(p)=(h)/(mv) The de Broglie relaion that the wavelength of a particle should decrease as its velocity increases. It also implies that for a given velocity heavier particles should have shorter wavelength than lighter particles.The 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 expermental confirmation of the de Broglie relation was obtained when Davission and Germer in 1927, observed. As diffraction is a characteristic property of waves, hence the beam of electrons behave as a wave as proposed by de Broglie. 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 can determine its position. The converse is also true. 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 uncertainty in the position, Deltax and the uncertainty in the momentum Delta(mv) must be greater than or equal to (h)/(4pi), i.e., Deltax Delta(mv)ge(h)/(4pi) The correct order of wavelength of Hydrogen (._(1)H^(1)) Deuterium (._(1)H^(2)) and Tritium (._(1)H^(3)) moving with same kinetic energy is :
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