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(a)A beam of 450 nm light is incident on a metal having work function 2.0 eV and placed in a magnetic field B. The most energetic electron emitted perpendicular to the field are bent in circular are of radius 20 cm. Find the value of B. (b) A small plate of metal (work function =1.17 eV) is placed at a distance of 2 m from a monochromatic light source of wavelength 4.8xx10^(-7) m and power 1.0 W. The light falls normally on the plate. Find the number of photons striking the metal plate per square meter per second. If a constant uniform magnetic field of strength 10^(-4) T is applied parallel to the metal surface, find the radius of the largest circular path following by the emitted photoelectrons. |
Answer» Solution :(a)  `E=(1242)/(lambda(nm))eV =(1242)/(450) =2.76 eV` `E=phi + K_(max) implies 2.76 = 2 + K_(max)` `K_(max) =0.76 eV` `R=(mv)/(Bq) =(SQRT(2mK_(max)))/(eB)` `B=(sqrt(2mK_(max)))/(eR) = (sqrt(2xx9.1xx10^(-31)xx0.76xx1.6xx10^(-19)))/(1.6xx10^(-19)xx0.2)` `=(1)/(0.2) sqrt((2xx9.1xx10^(-31)xx0.76)/(1.6xx10^(-19)))` `=(1)/(0.2)xx2.94xx10^(-6) =14.7xx10^(-6) T` (b) Intensity of light at distance r from POINT source `I=(P)/(4PI r^(2)) =n(hc)/(lambda)` `n=(I lambda)/(hc) =(P lambda)/(4 pi r^(2) hc) = (1xx4.8xx10^(-7))/(4pi(2)^(2)xx6.6xx10^(-34)xx3xx10^(8))` `=4.8xx10^(16)` `E=(1242)/(lambda(nm))eV =(1242)/(480) =2.59 eV` `E= phi + K_(max) implies 2.59=1.17+K_(max)` `K_(max) =1.42 eV` `R=sqrt(2mK_(max))/(eB) =(sqrt(2xx9.1xx10^(-31)xx1.42xx1.6xx10^(-19)))/(1.6xx10^(-19)xx10^(-4))` `=4xx10^(-2)m` |
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