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Consider two separate ideal gases of ele...

Consider two separate ideal gases of electrons and protons having same number of particles . The temperature of both the gases are same .The ratio of the uncertainty in determining the position of an electron to that of a proton is proportional to :

A

`sqrt((m_p)/(m_e))`

B

`(m_p)/(m_e)`

C

`((m_p)/(m_e))^(3/2)`

D

`sqrt((m_e)/(m_p))`

Text Solution

Verified by Experts

The correct Answer is:
A
`K.E.=3/2 kT`
`implies (p^2)/(2m)=3/2 kT`
`implies P=sqrt(3kTm)`
For Heisenberg uncertainty principle
`therefore Delta x. DeltaP=(h)/(4pi)`
`Delta x=(h)/(4 pi Delta P)=(h)/(4pi sqrt(3kTm))`
`therefore Delta x prop (1)/(sqrtm)`
`therefore (DeltaX_e)/(Delta X_p)=sqrt((m_p)/(m_e))`
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