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.)
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
`m_e = 9.11*10^-31` kg
Putting the values (in SI units) in the uncertainty relation:
= `3.35*10^-4` m/s.
Therefore, the value of n is 4.