JEE Main · 2021 · 31 Aug 2021 · Shift 2 · Modern Physics

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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) $\frac{m _{e}}{m _{p}}$
(B) $\frac{m _{p}}{m _{e}}$ ✓ Correct
(C) $\frac{m _{p}}{m _{e}}$
(D) $(\frac{m _{p}}{m _{e}})^{3/2}$

Answer: (B)

Solution

At temperature

T

each particle has thermal momentum of order

p = 3 m k_{B} T \propto m

. The position uncertainty follows from

Δ x Δ p \sim ℏ

, so

Δ x \propto \frac{1}{p} \propto \frac{1}{m}

. The ratio for the electron and the proton is therefore

\frac{Δ x _{e}}{Δ x _{p}} \propto \frac{m _{p}}{m _{e}} .

JEE Main · 2021 · 31 Aug 2021 · Shift 2 · Single correct option

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