What is the work function of the metal if the light of wavelength $4000 \stackrel{\circ}{\mathrm{~A}}$ generates photoelectrons of velocity $6 \times 10^{5} \mathrm{~ms}^{-1}$ from it? (Mass of electron $=9 \times 10^{-31} \mathrm{~kg}$ Velocity of light $=3 \times 10^{8} \mathrm{~ms}^{-1}$ Planck's constant $=6.626 \times 10^{-34} \mathrm{Js}$ Charge of electron $=1.6 \times 10^{-19} \mathrm{JeV}^{-1}$ )

JEE Main · 2019 · 12 Jan 2019 · Shift 1 · Atomic Structure

What is the work function of the metal if the light of wavelength

4000 A \circ

generates photoelectrons of velocity

6 \times 1 0^{5} ms^{- 1}

from it?
(Mass of electron

= 9 \times 1 0^{- 31} kg

Velocity of light

= 3 \times 1 0^{8} ms^{- 1}

Planck's constant

= 6.626 \times 1 0^{- 34} Js

Charge of electron

= 1.6 \times 1 0^{- 19} JeV^{- 1}

)

Answer: (C)

By Einstein's photoelectric equation the photon energy splits into the work function and the electron's kinetic energy,

\frac{h c}{λ} = ϕ + \frac{1}{2} m v^{2}

. The photon of wavelength

4000 \overset{˚}{A}

carries

\frac{( 6.626 \times 1 0 ^{- 34} ) ( 3 \times 1 0 ^{8} )}{4000 \times 1 0 ^{- 10}} = 4.97 \times 1 0^{- 19} J

, and the ejected electron has

\frac{1}{2} (9 \times 1 0^{- 31}) (6 \times 1 0^{5})^{2} = 1.62 \times 1 0^{- 19} J

. The work function is the difference,

4.97 \times 1 0^{- 19} - 1.62 \times 1 0^{- 19} = 3.35 \times 1 0^{- 19} J

, which on dividing by

1.6 \times 1 0^{- 19}

comes to about

2.1 eV

JEE Main · 2019 · 12 Jan 2019 · Shift 1 · Single correct option