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Structure of Atom — Chemistry STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceChemistryStructure of Atom2 Marks
Question
When would the wavelength associated with an electron be equal to the wavelength associated with a proton? Mass of electron $=9.1095 \times 10^{-28} \mathrm{~g} ;$ Mass of proton $=1.6725 \times 10^{-24} \mathrm{~g} \cdot \mathrm{OR}$
Calculate the velocity condition for the wavelength associated with a moving electron to be equal to the wavelength associated with a moving proton.
(Mass of electron $=9.11 \times 10^{-48} \mathrm{~g} ;$ Mass of proton $=1.67 \times 10^{-24} \mathrm{~g} ; \mathrm{h}=6.6 \times 10^{-34} \mathrm{Js} ; \mathrm{J}=\mathrm{kg} / \mathrm{m}^2 \mathrm{~s}^{-2}$. 
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Answer

$\lambda_{\mathrm{e}}=\frac{\mathrm{h}}{\mathrm{~m}_{\mathrm{e}} \mathrm{~V}_{\mathrm{e}}}$
$\lambda_{\mathrm{p}}=\frac{\mathrm{h}}{\mathrm{~m}_{\mathrm{p}} \mathrm{~V}_{\mathrm{p}}}$
$\Rightarrow \lambda_{\mathrm{e}}=\lambda_{\mathrm{p}}$
$\lambda_{\mathrm{e}}=\text { wavelengh of electron }$
$\lambda_{\mathrm{p}}=\text { wavelength of proton }$
$\text { Where, } \mathrm{m}_{\mathrm{e}}=\text { mass of electron }$
$\mathrm{m}_{\mathrm{p}}=\text { mass of proton }$
$\mathrm{V}_{\mathrm{e}}=\text { velocity of electron }$
$\mathrm{V}_{\mathrm{p}}=\text { velocity ofproton, }$
$\Rightarrow \mathrm{m}_{\mathrm{e}} \mathrm{~V}_{\mathrm{e}}=\mathrm{m}_{\mathrm{p}} \mathrm{~V}_{\mathrm{p}}$
$\Rightarrow \frac{\mathrm{~V}_{\mathrm{e}}}{\mathrm{~V}_{\mathrm{p}}}=\frac{\mathrm{m}_{\mathrm{p}}}{\mathrm{~m}_{\mathrm{e}}}=\frac{1.6725 \times 10^{-24}}{9.1095 \times 10^{-28}}=1836$
$\Rightarrow \mathrm{~V}_{\mathrm{e}}=1836 \mathrm{~V}_{\mathrm{p}}$

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