Given that,

B = B₀[sin (3.14 $$ \times $$ 10⁷) ct + sin(6.28 $$ \times $$ 10⁷) ct]

This light wave is non-monochromotic wave as here is two different frequency in the magnetic field.

Given work function ($$\phi $$) = 4.7 eV

Question says to find the maximum kinetic energy, so we have to use maximum frequency among the available frequency.

As,

K_max = E_max $$-$$ $$\phi $$

Emax = hF

= h $$ \times $$ $${\omega \over {2\pi }}$$

= 6.6 $$ \times $$ 10^$$-$$34 $$ \times $$ $${{6.28 \times {{10}^7} \times 3 \times {{10}^8}} \over {2\pi }}$$

= 6.6$$ \times $$ 3 $$ \times $$ 10^$$-$$19 J

= $${{6.6 \times 3 \times {{10}^{ - 19}}} \over {1.6 \times {{10}^{ - 19}}}}eV$$

= 12.375 $$eV$$

$$ \therefore $$  K_max = 12.375 $$-$$ 4.7

= 7.675 $$eV$$

$$ \simeq $$  7.7 $$eV$$