Given,
\( \lambda=4000 \mathrm{~Å} \)
\(v=6 \times 10^5 \mathrm{~ms}^{-1}\)
As,
\(h v=w+k \cdot E\)
\(\Rightarrow \frac{h c}{\lambda}=w+k \cdot E\)
\(\Rightarrow \frac{6.626 \times 10^{-34} \mathrm{Js} \times 3 \times 10^8 \mathrm{~m} / \mathrm{s}}{4000 \times 10^{-10}}=w+\frac{1}{2} \mathrm{mv}^2\)
\(\Rightarrow 5 \times 10^{-19}={w}+\frac{1}{2} \times\left(9 \times 10^{-31} \mathrm{~kg}\right) \times\left(6 \times 10^5 \mathrm{~m} / \mathrm{s}\right)^2\)
\( \Rightarrow w=\left(5 \times 10^{-19}\right) \mathrm{J}-\left(1.62 \times 10^{-19}\right) \mathrm{J} \)
\(\Rightarrow w=3.38 \times 10^{-19} \mathrm{~J} \)
\(\Rightarrow w=\frac{3.38 \times 10^{-19} \mathrm{~J}}{1.6 \times 10^{-19} \mathrm{J/ev}}\)
\(\Rightarrow w=2.11\mathrm {~ ev}\)
