A photosensitive surface has work function ϕ . If photon of energy 3 ϕ falls on this surface, the electron comes out with maximum velocity of 4 × 1 0 6 m / s . When photon energy is increased to 7 ϕ t

Question

A photosensitive surface has work function ϕ . If photon of energy 3 ϕ falls on this surface, the electron comes out with maximum velocity of 4 × 1 0 6 m / s . When photon energy is increased to 7 ϕ then maximum velocity of photoelectron will be

TestHub · Accepted Answer

According to Einstein's photoelectric equation:

$K_{m a x} = E - ϕ$

For the first case, $E_{1} = 3 ϕ$ :

$\frac{1}{2} m v_{1}^{2} = 3 ϕ - ϕ = 2 ϕ$

For the second case, $E_{2} = 7 ϕ$ :

$\frac{1}{2} m v_{2}^{2} = 7 ϕ - ϕ = 6 ϕ$

Taking the ratio of the two equations:

$\frac{v _{2}^{2}}{v _{1}^{2}} = \frac{6 ϕ}{2 ϕ} = 3$

$v_{2} = 3 v_{1}$

Substituting $v_{1} = 4 \times 1 0^{6} m/s$ :

$v_{2} = 43 \times 1 0^{6} m/s$

Answer: $43 \times 1 0^{6} m / s$

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