Consider two separate ideal gases of electrons and protons having same number of particles. The temperature…

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:
  1. mpme
  2. mpme
  3. mpme32
  4. memp

Solution

K.E.=32kT
p22m=32kT
p=3kT m
From Heisenberg uncertainty principle
 ΔxΔp=h4π
Δx=h4πΔp=h4π3kTm
 Δx1m
 ΔxeΔxp=mpme

Asked in: JEE Main 2021 (31 Aug Shift 2)

Practice more Dual Nature of Matter questions on Aicharya