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:-

Option 1 -

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

Option 2 -

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

Option 3 -

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

Option 4 -

${(\frac{m_{p}}{m_{e}})}^{3 / 2}$

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1 Answer

Answered by

Vishal Baghel | Contributor-Level 10

a month ago

Correct Option - 2

Detailed Solution:

Heisenberg uncertainty principle :

$\begin{array}{l} \Rightarrow Δ x Δ p \geq ? \\ \Rightarrow Δ x (m Δ v) \geq ? \end{array}$

$\Rightarrow Δ x (m \sqrt[]{\frac{3 R T}{m}}) \geq ?$

$\Rightarrow Δ x \propto \frac{1}{\sqrt[]{m}}$

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