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Uncertainty in the position of an electr...

Uncertainty in the position of an electron mass ` (9. 1 xx 10^(31) kg)` moving with a velocity ` 300 ms^(-1)` accurate uptp ` 0.001 %` will be :

A

`19.2xx10^(-2)m`

B

`5.76xx10^(-2)m`

C

`1.92xx10^(-2)m`

D

`3.84xx10^(-2)m`

Text Solution

Verified by Experts

The correct Answer is:
C
According to Heisenberg’s uncertainty principle,
`Delta x xx Deltap=(h)/(4pi)" "Deltax. (m. Deltav)=(h)/(4pi) rArr Deltax =(h)/(4pim.Deltav)`
Here `Deltav=(0.001)/(100)xx300=3xx10^(-3) ms^(-1)`
`therefore" "Detalx=(6.63xx10^(-34))/(4xx3.14xx9.1xx10^(-31)xx3xx10^(-3))=1.92xx10^(-2)m`
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