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Structure of Atom — Chemistry STD 11 Science — Question

Rajasthan 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 × 10-28g; Mass of proton = 1.6725 × 10-24g.

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 × 10-48g; Mass of proton = 1.67 × 10-24g; h = 6.6 × 10-34Js; J = kg/ m2s-2).

✓

Answer

$\lambda_\text{e}=\frac{\text{h}}{\text{m}_\text{e}\text{V}_\text{e}}$
$\lambda_\text{p}=\frac{\text{h}}{\text{m}_\text{p}\text{V}_\text{p}}$
$\Rightarrow\lambda_\text{e}=\lambda_\text{p}$
$\lambda_\text{e}=$ wavelengh of electron
$\lambda_\text{p}=$ wavelength of proton
Where, me = mass of electron
mp = mass of proton
Ve = velocity of electron
Vp = velocity ofproton,
$\Rightarrow\text{m}_\text{e}\text{V}_\text{e}=\text{m}_\text{p}\text{V}_\text{p}$
$\Rightarrow\frac{\text{V}_\text{e}}{\text{V}_\text{p}}=\frac{\text{m}_\text{p}}{\text{m}_\text{e}}=\frac{1.6725\times10^{-24}}{9.1095\times10^{-28}}=1836$
$\Rightarrow\text{V}_\text{e}=1836\text{V}_\text{p}$

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