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Correct option is A)

We hav to take two cases :

Case I....$v_{0}=1.656$

$v=5×10_{14}Hz$

Case II....$v_{0}=0$

$v=1×10_{14}Hz$

We know ;

a) $eV_{0}=hν−w_{0}$

$1.656e=h×5×10_{−14}−w_{0}$........(1)

$0=5h×10_{14}−5w_{0}$ ........(2)

$1.656e=4w_{0}$

$⇒w_{0}=41.656 ev=0.414ev$

b) Putting value of $w_{0}$ in equation (2)

$⇒5w_{0}=5h×10_{14}$

$⇒5×0.414=5×h×10_{14}$

$⇒h=4.414×10_{−15}$ ev-s

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