KVPY SX SB Exam 2016 Question Paper

Question : 24 of 120

Marks: +1, -0

Photons of wavelength λ are incident on a metal. The most energetic electrons ejected from the metal are bent into a circular arc of radius R by a perpendicular magnetic field having a magnitude B. The work function of the metal is (Where symbols have their usual meanings) -

${hc}/λ-m_e+{e^2B^2R^2}/{2m_e}$
${hc}/λ+2m_e({eBR}/{2m_e})^2$
${hc}/λ-m_eC^2-{e^2B^2R^2}/{2m_e}$
${hc}/λ-2m_e({eBR}/{2m_e})^2$

Validate

Solution:

R={mv}/{qB}

V={qBR}/m={eBR}/m_e

{hc}/λ-ϕ=\KE_\max

(Einstein photo electric equation)

ϕ={hc}/λ-\KE_\max

={hc}/λ-1/2m_e({eBR}/m_e)^2

={hc}/λ- 2m_e({eBR}/{2m_e})^2

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