Q 12-11-119JEE MainJEE Main 2021 (31 Aug, Shift 2)Medium
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:
Answer: (A) $\sqrt{\dfrac{m_p}{m_e}}$
At the same temperature, the typical momentum is $p = \sqrt{3mkT} \propto \sqrt m$; take $\Delta p \sim p$.
Uncertainty principle: $\Delta x \propto \dfrac{1}{\Delta p} \propto \dfrac{1}{\sqrt m}$.
$$\frac{\Delta x_e}{\Delta x_p} = \sqrt{\frac{m_p}{m_e}}$$
Solution by Sreeraj P, M.Sc Physics