A metal surface is exposed to 500 nm radiation. The threshold frequency of the metal for photoelectric current is 4.3 $\times$ 10¹⁴ Hz. The velocity of ejected electron is ____________ $\times$ 10⁵ ms^$-$1 (Nearest integer)

[Use : h = 6.63 $\times$ 10^$-$34 Js, m_e = 9.0 $\times$ 10^$-$31 kg]

$\upsilon$ : speed of electron having max. K.E.<br><br> $\Rightarrow$ from Einstein equation : E = $\phi$ + K.E._max<br><br>$\Rightarrow {{hc} \over \lambda } = h{\upsilon _0} + {1 \over 2}m{v^2}$<br><br>$$ \Rightarrow {{6.63 \times {{10}^{ - 34}} \times 3 \times {{10}^8}} \over {500 \times {{10}^{ - 9}}}} = 6.63 \times {10^{ - 34}} \times 4.3 \times {10^{14}} + {1 \over 2}m{v^2}$$<br><br>$$ \Rightarrow {{6.63 \times 30 \times {{10}^{ - 20}}} \over 5} = 6.63 \times 4.3 \times {10^{ - 20}} + {1 \over 2}m{v^2}$$<br><br>$$ \Rightarrow 11.271 \times {10^{ - 20}}J = {1 \over 2} \times 9 \times {10^{ - 31}} \times {\upsilon ^2}$$<br><br>$\Rightarrow$ $\upsilon$ = 5 $\times$ 10⁵ m/sec.