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JEE Main 2021 (31 Aug, Shift 2) · Davisson-Germer, Uncertainty, Compton & X-Rays

Davisson-Germer, Uncertainty, Compton & X-Rays question from JEE Main 2021 (31 Aug, Shift 2)

Q7JEE Main 2021 · 31 AUG · SHIFT 2Medium

Davisson-Germer, Uncertainty, Compton & X-Rays

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

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Answer: (c)

  1. Uncertainty principle: Δx≈h4πΔp\Delta x \approx \frac{h}{4\pi \Delta p}, take Δp∼p\Delta p \sim p.
  2. Same temperature: p=3mkT⇒p∝mp = \sqrt{3mkT} \Rightarrow p \propto \sqrt{m}
  3. Δx∝1m⇒ΔxeΔxp=mpme\Delta x \propto \frac{1}{\sqrt{m}} \Rightarrow \frac{\Delta x_e}{\Delta x_p} = \sqrt{\frac{m_p}{m_e}}
  4. So the answer is (c).
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