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If the uncertainties in the measuremen...

If the uncertainties in the measurement of position and momentum of an electron are equal, calculate the uncertainty in measuring the velocity.

A

` 1/m sqrt h/(pi)`

B

` sqrt h/(pi)`

C

`1/( 22m) sqrt h/(pi)`

D

`sqrt h/(2pi)`

Text Solution

Verified by Experts

The correct Answer is:
C
According to Heisenbegr uncetainty principle
` Delta p. Delta x le h/( 4 pi)`
or ` Delta u . Delta x. m le h/( 4 pi)`
` or ( m delta u) ^2 le h/( 4 pi) (:. Delta x =Delta p) `
or ` Delta u = 1/( 2m) sqrt h/(pi)`.
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Werner Heisenberg considered the limits of how precisely we can measure the properties of an electron or other microscopic particle. He determined that there is a fundamental limit to 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 true. this is summed up in what we now call the Heisenberg uncertainty principal. The equation is Deltax.Delta(mv) ge (h)/(4pi) The uncertainty is the position or in the momentum of a macroscopic object like a baseball is too small to observe. However, the mass of microscopic object such as an electron is small enough for the uncertainty to be relatively large and significant. If the uncertainties in position and momentum are equal, the uncertainty in the velocity is:

Werner Heisenberg considered the limits of how precisely we can measure the properties of an electron or other microscopic particle. He determined that there is a fundamental limit to 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 also true. This is summed up in what we now call the Heisenberg uncertainty principle. The equation si deltax.delta (mv)ge(h)/(4pi) The uncertainty in the position or in the momentum of a marcroscopic object like a baseball is too small to observe. However, the mass of microscopic object such as an electon is small enough for the uncertainty to be relatively large and significant. If the uncertainties in position and momentum are equal, the uncertainty in the velocity is :

P BAHADUR-ATOMIC STRUCTURE-Exercise 3A
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  4. The mass fo 1 mole pghoton of wavelength 589 nm is :

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  5. Number of degenerate orbitals in a level of H-atom having En = (Rh)/9...

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  6. The orientiation of an atomic orbital is governed by :

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  8. The speed of an electron having its wavelength being equal to speed ca...

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  9. The differnce between nth and (n+1) the Bohr radius of B atom is equa...

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  10. Fill up a sutiable figure in each set in respective choices for psi(3...

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  11. If the uncertainties in the measurement of position and momentum ...

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  12. Ratio of m^(th) wavelength of Lyman series in H-atom is equal to:

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  13. IE1 for (H) and De are 13.6 eV 1 and 24.6 eV respectively . Thus enr...

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  14. The circumfernce fo n^(th) orbit in H-atom can be expressed in tems fo...

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  15. Ration of m^(th) to n^(th) wavelength of Balmer series in H-atom is eq...

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  16. An excited hydrogen atom returns to the ground state . The wavelength ...

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  17. When an electron fo mass 6 m and charge 6e moves with a velocity of 7u...

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  18. If lambda0 is the Threshold wavelength of a metal for photoelencron e...

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  19. The emission of electrons from a metal surface exposed to light ra...

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  20. The number fo electrons present in 1 cm^3 of Mg (density of . (12)M...

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