What is the work function of the metal if the light of wavelength $4000 A^{0}$ Generates photoelectrons of velocity $6 \times 10^{5} m / s$ From it? (Mass of electron $= 9 \times 10^{- 31} k g$ , Velocity of light $= 3 \times 10^{8} m s^{- 1}$ Planck’s constant $= 6.626 \times 10^{- 34} J s$ Charge of electron $= 1.6 \times 10^{- 19} c o u l o m b s$ )

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2.1 eV

3.1 eV

5.0 eV

0.9 eV

answer is C.

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Detailed Solution

$E = h v = \frac{h c}{λ}$

$E = \frac{6.626 \times 10^{- 34} \times 3 \times 10^{8}}{4000 \times 10^{- 10}} = 4.97 \times 10^{- 19} J = \frac{4.97 \times 10^{- 19} J}{1.6 \times 10^{- 19} J e V^{- 1}} = 3.1 e V$

$K E = \frac{1}{2} m v^{2} = \frac{1}{2} \times 9 \times 10^{- 31} k g \times {(6 \times 10^{5} m s^{- 1})}^{2} = 1.62 \times 10^{- 19} J [1 J = k g . m^{2} s^{- 2}] = 1 e V$