Dual Nature of Matter

JEE Main level, single correct, medium

104 of 200

Question 104 of 200

A monochromatic light is incident on a metallic plate having work function ϕ\phi. An electron, emitted normally to the plate from a point AA with maximum kinetic energy, enters a constant magnetic field, perpendicular to the initial velocity of electron. The electron passes through a curve and hits back the plate at a point BB. The distance between A and B is :
(Given : The magnitude of charge of an electron is e and mass is m,h\mathrm{m}, \mathrm{h} is Planck's constant and c is velocity of light. Take the magnetic field exists throughout the path of electron)

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Answer: (C) 8 m(hcλ−ϕ)/eB\sqrt{8 \mathrm{~m}\left(\frac{\mathrm{hc}}{\lambda}-\phi\right)} / \mathrm{eB}

KEmax⁡=hcλ−ϕp=2mKmax⁡p=2 m(hcλ−ϕ)dA−B=2R=2[pqB]\begin{aligned} & \mathrm{KE}_{\max }=\frac{\mathrm{hc}}{\lambda}-\phi \\ & \mathrm{p}=\sqrt{2 \mathrm{mK}_{\max }} \\ & \mathrm{p}=\sqrt{2 \mathrm{~m}\left(\frac{\mathrm{hc}}{\lambda}-\phi\right)} \\ & \mathrm{d}_{\mathrm{A}-\mathrm{B}}=2 \mathrm{R} \\ & =2\left[\frac{\mathrm{p}}{\mathrm{qB}}\right]\end{aligned}
dAB=22 m(hcλ−ϕ)eB=8 m(hcλ−ϕ)eB\mathrm{d}_{\mathrm{AB}}=\frac{2 \sqrt{2 \mathrm{~m}\left(\frac{\mathrm{hc}}{\lambda}-\phi\right)}}{\mathrm{eB}}=\frac{\sqrt{8 \mathrm{~m}\left(\frac{\mathrm{hc}}{\lambda}-\phi\right)}}{\mathrm{eB}}

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