Dual Nature of Matter

JEE Main level, single correct, medium

60 of 200

Question 60 of 200

An α\alpha particle and a proton are accelerated from rest by a potential difference of 200V200V. After this, their de Broglie wavelengths are λα{\lambda }_{\alpha } and λp{\lambda }_{p} respectively. The ratio λpλα\dfrac{{\lambda }_{p}}{{\lambda }_{\alpha }} is :

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Answer: (C) 2.82.8

λ=hp=h2mqV\lambda =\dfrac{h}{p}=\dfrac{h}{\sqrt{2mqV}}
⇒λpλα=mαqαmpqp=4mp×2emp×e=8=22\Rightarrow \dfrac{{\lambda }_{p}}{{\lambda }_{\alpha }}=\sqrt{\dfrac{{m}_{\alpha }{q}_{\alpha }}{{m}_{p}{q}_{p}}}=\sqrt{\dfrac{4{m}_{p}\times 2e}{{m}_{p}\times e}}=\sqrt{8}=2\sqrt{2}=22=2\sqrt{2}
⇒λpλα=2×1.4=2.8\Rightarrow \dfrac{{\lambda }_{p}}{{\lambda }_{\alpha }}=2\times 1.4=2.8

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