Medium MCQ +4 / -1 PYQ · JEE Mains 2021

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 :-

  1. A ${\left( {{{{m_p}} \over {{m_e}}}} \right)^{3/2}}$
  2. B $\sqrt {{{{m_e}} \over {{m_p}}}}$
  3. C $\sqrt {{{{m_p}} \over {{m_e}}}}$ Correct answer
  4. D ${{{m_p}} \over {{m_e}}}$

Solution

$\Delta x\,.\,\Delta p \ge {h \over {4\pi }}$<br><br>$\Delta x = {h \over {4\pi m\Delta v}}$<br><br>$v = \sqrt {{{3KT} \over m}}$<br><br>${{\Delta {x_e}} \over {\Delta {x_p}}} = \sqrt {{{{m_p}} \over {{m_e}}}}$

About this question

Subject: Physics · Chapter: Dual Nature of Matter and Radiation · Topic: Photoelectric Effect

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