A photon with energy of $$4.9$$ eV ejects photoelectrons from tungsten. When the ejected electron enters a constant magnetic field of strength B $$=$$ $$2.5$$ mT at an angle of $$60$$° with thee field direction, the maximum pitch of the helix described by the electron is found to be $$2.7$$ mm. Find the $$work-function$$ of the metal in $$electron-volt$$. Given that, specific charge of electron is $$1.76$$×$$1011$$ $$C/$$ kg.

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Infinity Learn · Accepted Answer

Pitch of helical path, $$p=(vcos$$⁡θ$$)T=vT2$$.  as θ$$=60$$∘                   $$T=2$$$$π$$$$mBq=2$$$$π$$Bα α$$=qm$$∴  $$p=$$πvBα or   $$v=B$$αpπ    ........(i)       $$KE$$$$=12mv2=E$$−W∴   $$W=E$$−$$12mv2$$   .........(ii)Substituting$$ value of v from Eq. $$(i) in Eq. (ii),we $$getW=4.9$$−$$12$$               $$9.1$$×$$10$$−$$31$$×$$2.5$$×$$10$$−$$321.76$$×$$10112$$                   ×$$2.7$$×$$10$$−$$32$$$$π$$$$2$$×$$1.6$$×$$10$$−$$19$$                  $$=(4.9$$−$$0.4)eV=4.5eV$$

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