Explanation:
According to the Einstein's equation
\(K E_{\max }=h v_{0}-\phi_{0}\)
Where \(K E_{\max }=\) maximum kinetic energy and
\(\phi_{0}=\text { work function }\)
Initially \(h{v_0} = 0.4 + {\phi _0}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\)
When the frequency of incident radiation os increased by \(30 \%\), then
\(1.3hv = 0.9 + {\phi _0}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(2)\)
Solving eq.(1) and eq.(2), we get
\(0.3{\phi _0} = 0.9 - 1.3(0.4)\)
\(\therefore {\phi _0} = \frac{{0.38}}{{0.3}} = 1.267eV\)