In an experiment on photoelectric effect, the emitter and the collector plates are placed at a separation of 10cm and are connected through an ammeter without any cell. A magnetic field B exists parallel to the plates. The work function of the emitter is 2.39 e V and the light incident on it has wavelengths between 400nm and 600nm. Find the minimum value of B for which the current registered by the ammeter is zero. Neglect any effect of space charge.

Explanation

Here `phi_0 = 2.39 eV `
` lambda_1 = 400nm` ,
`lambda_2 = 600 nm `
for b to be minimum, energy should be maximum
` :. lambda should be minimum
` E = hc / lambda - phi_0`
` = 1242 / 400 - 2.39 `
` = 3.105 - 2.39 = 0.715 eV.`
The presence of magnetic field will bend the beam . There will be no current if the electron does not reach the other plates.
` r = mv / qB `
`rArr = (sqrt 2 mF / qB ) `
` rArr 0.1 =(sqrt 2 xx 9.1 xx 10^(-31) xx 1.6 xx 10^(19) xx 0.715 / 1.6xx 10^(-20) xx B ) `
` B = (sqrt 2 xx 9.1 xx 1.6 xx 0.715 xx 10^(-50) / 1.6xx 10^(-20) ) `
`= (sqrt 2 xx 9.1 xx 1.6 xx 0.715 / 1.6 ) xx 10^(-5)`
` = 2.85 xx 10^(-5) `