A particle is moving 5 times as fast as an electron. The ratio of the de-Broglie wavelength of the particle to that of the electron is 1.878 $\times$ 10–4. The mass of the particle is close to
Solution
Let mass of particle = m
<br><br>Let speed of e<sup>–</sup>
= V
<br><br>$\therefore$ speed of particle = 5V
<br><br>de-broglie wavelength $\lambda$<sub>d</sub> = ${h \over P} = {h \over {mv}}$
<br><br>$\therefore$ ($\lambda$<sub>d</sub>)<sub>P</sub> = ${h \over {m\left( {5V} \right)}}$ ....(1)
<br><br>and ($\lambda$<sub>d</sub>)<sub>e</sub> = ${h \over {{m_e}\left( V \right)}}$ ....(1)
<br><br>According to question
<br><br>$${{{{\left( {{\lambda _d}} \right)}_P}} \over {{{\left( {{\lambda _d}} \right)}_e}}} = {{{m_e}} \over {5m}}$$ = 1.878 $\times$
10<sup>–4</sup>
<br><br>$\Rightarrow$ m = ${{{m_e}} \over {5 \times 1.874 \times {{10}^{ - 4}}}}$
<br><br>= ${{9.1 \times {{10}^{ - 31}}} \over {5 \times 1.874 \times {{10}^{ - 4}}}}$
<br><br>= 9.7 $\times$ 10<sup>–28</sup> kg
About this question
Subject: Physics · Chapter: Dual Nature of Matter and Radiation · Topic: de Broglie Hypothesis
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