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 the 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 `1.76xx10^11 C/(kg)`.

Explanation

Pitch of the helix is given by
`y=(vcostheta).T=v(cos60)T=vT//2`
Where time period of circular motion
`T=(2pim)/(eB)`
Pitch `y=((v2pim)/(Be))vcos60^(@)=(pimv//Be)`
`:. KE=(1)/(2)mv^(2)=(1)/(2)m((Bey)/(pim))^(2)`
Using Einstein 's equation
`(1)/(2)mv^(2)=hv-phi`
`phi=hv-(1)/(2)m((Bey)/(pim))^(2)=[4.9-(1)/(2)((m)/(e))((Bey)/(pim))^(2)]`electron-volts
`=[4.9-(1)/(2)(B^(2)y^(2))/(4pi^(2))((e)/(m))]"electron-volt"=(4.9-0.4)eV=4.5eV`