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RESPECTED SIR/MADAM, PLEASE HELP ME OUT. An electron is allowed to move freely in a...

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user8235304 | Student, Grade 11 | Valedictorian

Posted May 29, 2013 at 8:04 AM via web

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RESPECTED SIR/MADAM,

PLEASE HELP ME OUT.

An electron is allowed to move freely in a closed cubic box of length of side 10 cm.The maximum uncertainty in its velocity is 3.35 * 10^-n m/s,Find the value of n.

(Remember n should be an integer.)

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llltkl | College Teacher | Valedictorian

Posted May 29, 2013 at 8:59 AM (Answer #1)

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According to Heisenberg’s uncertainty principle, it is impossible to know simultaneously both the conjugate properties of a particle accurately.  

For example, the position and momentum of a moving particle are interdependent and thus conjugate properties also, they can not be determined with absolute exactness or certainty at the same time. There remains a minimum error in determining the two properties, which is given by:

`Deltax*Deltap>=h/(4pi)` ` `

`rArr ``Deltax*mDeltav>=h/(4pi)`` `

Where ∆x is the uncertainty in position, ∆p, uncertainty in momentum and ∆v, in velocity; h is the Planck’s constant.

 

The electron is confined in a cubic box having length of side 10 cm = 0.1 m.

The maximum uncertainty in measuring its position will be the maximum distance it is allowed to travel, i.e. the body diagonal of the cubic box, thus

`Deltax=sqrt3*0.1` m.

`m_e = 9.11*10^-31` kg

Putting the values (in SI units) in the uncertainty relation:

`Deltav=(6.626*10^-34)/(9.11*10^-31*4*pi*sqrt3*0.1)` m/s

= `3.35*10^-4` m/s.

 

Therefore, the value of n is 4.

 

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