When the light of frequency 2 ν 0 (where ν 0 is threshold frequency), is incident on a metal plate, the maximum velocity of electrons emitted is v 1 . When the frequency of the incident radiation is increased to 5 ν 0 , the maximum velocity of electrons emitted from the same plate is v 2 . The ratio of v 1   t o   v 2 is

Step-by-step solution

From Einstein's equation of Photoelectric effect, we can write For case 1: 1 2 mv 1 2 = 2 hν 0 − hν 0   ⇒ 1 2 mv 1 2 = hv 0 ... (i), where m is mass of electron, h is Planck's constant. For case 2: 1 2 mv 2 2 = 5 hν 0 − hν 0 ⇒ 1 2   mv 2 2 = 4 hν 0 ... (ii) From ( 1 ) and ( 2 ) v 1 v 2 = 1 4 = 1 2 . Hence, the ratio of v 1 and v 2 is 1 : 2 .