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Question

When a metal surface is illuminated by light of wavelengths 400 nm and 250 nm, the maximum velocities of the photoelectrons ejected are v and 2v respectively. The work function of the metal is (h = Planck’s constant, c = velocity of light in air)


A

2 hc×106J

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B

1.5 hc×106J

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C

hc×106J

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D

0.5 hc×106J

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Solution

The correct option is A

2 hc×106J


By using hcλ=W0+12mv2
hc400×109=W0+12mv2 (i)
and hc250×109=W0+12m(2v)2 (ii)
On solving (i) and (ii)
12mv2=hc3[1250×1091400×109] (iii)
From equation (i) and (iii) W0=2hc×106 J


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