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(C) According to Heisenberg's uncertainty principle,$\Delta x \cdot \Delta p \geq \frac{h}{4\pi}$.Since $\Delta p = m \Delta v$,we have $\Delta x \pro

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$\sqrt{\frac{m_{p}}{m_{e}}}$

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(C) According to Heisenberg's uncertainty principle,$\Delta x \cdot \Delta p \geq \frac{h}{4\pi}$.Since $\Delta p = m \Delta v$,we have $\Delta x \propto \frac{1}{m \Delta v}$.For an ideal gas,the root mean square velocity is $v_{rms} = \sqrt{\frac{3kT}{m}}$,so $\Delta v \propto \frac{1}{\sqrt{m}}$.Substituting this into the uncertainty relation: $\Delta x \propto \frac{1}{m \cdot (1/\sqrt{m})} = \frac{1}{\sqrt{m}}$.Therefore,the ratio of uncertainty in position is $\frac{\Delta x_e}{\Delta x_p} = \frac{1/\sqrt{m_e}}{1/\sqrt{m_p}} = \sqrt{\frac{m_p}{m_e}}$.

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