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JEE Main 201912 JanuaryMorning Shift
Exam
JEE Main
Year
2019
Date
12 January
Shift
Morning Shift
Subject
Chemistry
Chapter
Structure of Atom

JEE Main 2019 · 12 January · Morning Shift · Chemistry · Structure of Atom

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

What is the work function of the metal if the light of wavelength 4000Ao4000\overset{o}{A} generates photoelectrons of velocity 6×105ms−16 \times {10}^{5}{ms}^{- 1} from it?

(Mass of electron =9×10−31kg= 9 \times {10}^{- 31}kg, velocity of light =3×108ms−1= 3 \times {10}^{8}{ms}^{- 1}, Planck's constant =6.626×10−34Js= 6 .626 \times {10}^{- 34}Js, Charge of electron =6.626×10−34Js= 6 .626 \times {10}^{- 34}Js)

Options

  1. A0.9eV0 .9 eV
  2. B4.0eV4 .0 eV
  3. C3.1eV3 .1 eV
  4. D2.1eV2 .1 eV

Correct answer

D. 2.1eV2 .1 eV

Step-by-step solution

hcλ=hcλ0+12mv2\dfrac{hc}{\lambda} = \dfrac{hc}{{\lambda}_{0}} + \dfrac{1}{2}{mv}^{2}

hcλ0=hcλ−12mv2\dfrac{hc}{{\lambda}_{0}} = \dfrac{hc}{\lambda} - \dfrac{1}{2}{mv}^{2}

=6.626×10−34×3×1084000×10−10−12(9.1×10−31)×(6×105)2= \dfrac{6.626 \times {10}^{- 34} \times 3 \times {10}^{8}}{4000 \times {10}^{- 10}} - \dfrac{1}{2}\left(9.1 \times {10}^{- 31}\right) \times {\left(6 \times {10}^{5}\right)}^{2}

=6.626×3×10−194−9.1×6×62×10−21= \dfrac{6.626 \times 3 \times {10}^{- 19}}{4} - \dfrac{9.1 \times 6 \times 6}{2} \times {10}^{- 21}

=4.97×10−19−1.64×10−19= 4.97 \times {10}^{- 19} - 1.64 \times {10}^{- 19}

=3.33×10−19= 3.33 \times {10}^{- 19} Joule

Work function \left(\dfrac{hc}{{\lambda}_{0}}\right) = \dfrac{3 .33 \times {10}^{- 19}}{1 .6 \times {10}^{- 19}} = 2 .08 \approx 2 .1 eV
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