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 electrons emitted perpendicular to the field are bent in circular arcs of radius 20 cm. Find the value of B.

Explanation

The kinetic energy of the most energetic
electrons is
` K= (hc/ lambda)- varphi`
` =( 1242eV nm / 450 nm) - 2.0e V.`
` = 0.76 e V = 1.2 xx (10^-19)J`
` The linear momentum = mv = (sqrt(2mK)).`
` = (sqrt (2 xx (9.1 xx (10^-31) kg) xx (1.2 xx (10^-19)J)))`
` = 4.67 xx (10^-25) kg (ms^-1).`
` When a charged particle is sent perpendicular to
magnetic field, it goes along a circle of radius.
` r = (mv/ qB)`
` Thus, 0.20m = (4.67 xx (10^25)kg m (s^-1)/ (1.6 xx (10^-19)C)xx B).`
` or, B= (4.67 xx (10^-25)kg (ms^-1))/((1.6 xx (10^-19)C) xx (0.20m))= 1.46 xx (10^-5).`