a
\(\,{\left( {\frac{1}{2}m{\upsilon _{\max }}^2} \right)_1}\,\, = \,\,{(h{f})_1}\, - \,\,{\phi _0}\,\)

\( = \,\,3\phi \,\, - \,\,\phi \,\, = \,\,2\phi \,\,\,{\left( {\frac{1}{2}m{\upsilon _{\max }}^2} \right)_1}\,\,\)

\( = \,\,{(h{f})_2}\, - \,\,{\phi _0}\, = \,\,9\phi \,\, - \,\,\phi \,\, = \,\,\,8\phi \)

\(\therefore \,\,\,\frac{{{{\left( {\frac{1}{2}m{\upsilon _{\max }}^2} \right)}_2}}}{{{{\left( {\frac{1}{2}m{\upsilon _{\max }}^2} \right)}_1}}}\)

\( = \,\,\frac{{8\phi }}{{2\phi }}\,\, = \,\,4\,\,\,\,\frac{{{{({\upsilon _{\max }})}_2}}}{{{{({\upsilon _{\max }})}_1}}}\,\, = \,\,2\)

\(\therefore \,\,{({\upsilon _{\max }})_2}\, = \,\,2{({\upsilon _{\max }})_1}\)

\( = \,\,2\,\, \times \,\,6\,\, \times \,\,{10^6}\, = \,\,12\,\, \times \,\,{10^6}\,m/s\)