Magnetic Effects & Magnetism

JEE Main level, single correct, medium

157 of 276

Question 157 of 276

Radiation, with wavelength 6561A˚6561Å falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of 3×10−4T3\times {10}^{-4}T . If the radius of the largest circular path followed by the electrons is 10mm10mm , the work function of the metal is close to:

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Answer: (C) 1.1eV1.1eV

KEmax=E−ϕK{E}_{max}=E-\phi
=12400λ(inÅ)−ϕ=\dfrac{12400}{\lambda \left(inÅ\right)}-\phi (in eV)
∴r=2mKEeB∴r=\dfrac{\sqrt{2mKE}}{eB}
KEmax=r2e2B22mK{E}_{max}=\dfrac{{r}^{2}{e}^{2}{B}^{2}}{2m} (in J)
=r2eB22m=\dfrac{{r}^{2}e{B}^{2}}{2m} (in eV)
∴ϕ=124006556−r2eB22m∴\phi =\dfrac{12400}{6556}-\dfrac{{r}^{2}e{B}^{2}}{2m}
=1.1eV=1.1eV

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