A stream of photons with energy 4.4eV strike a metal surface with work function 3.5 eV. The electrons are ejected at an angle `45^(@)` with the normal to the surface. Uniform magnetic and electric field exist in the space outside the surface of metal as shown. Determine the value of pitch (in m) of helix in the `3^(rd)` revolution for electrons ejected maximum kinetic energy. Round off the answer to nearest integer. Intensity of electric field is `10^(-3)N//C` and magnetic field is `pixx10^(-6)`T. (Given : mass of electron `=9xx10^(-31)` kg, charge of electron `=1.6xx10^(-19)C`).

Answer

`0005`

Explanation

`u=sqrt((2k)/(m))`
`p_(3)=(u)/(sqrt(2))T+(1)/(2)(5at^(2))=(u)/(sqrt(2))((2pim)/(eB))+(5)/(2)((eE)/(m))((2pi m)/(eB))^(2)=(u sqrt(2)pi m)/(eB)+(10Epi^(2)m)/(e B^(2))`
`p_(3)=(pi m)/(eB)(u sqrt(2)+(10E pi)/(B))=(pi m)/(eB)(2sqrt((k)/(m))+(10Epi)/(B))`
`p_(3)=(pi m)/(eB)(2sqrt((k)/(m))+(10E pi)/(B))`
` B=pixx10^(-6)T`
` E=10^(-2)N//C`
`k_(max)=0.9 eV`
`p_(3)=(pim)/(eB)(-2sqrt(((9xx10^(-1))(16xx10^(-20)))/((9xx10^(-31))))+10(10^(-2))/(pixx10^(-6))pi)=(pi 9 xx10^(-31))/(16xx10^(-20).pixx10^(-6))(8sqrt(10^(+10))+10^(5))`
`=(9)/(16)xx10^(-5)(9xx10^(5))`
`p_(3)=(81)/(16)~~5m`