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JEE Advanced 2016Paper 1
Exam
JEE Advanced
Year
2016
Paper
Paper 1
Subject
Physics
Chapter
Dual Nature of Matter

JEE Advanced 2016 · Paper 1 · Physics · Dual Nature of Matter

In a historical experiment to determine Planck's constant, a metal...

In a historical experiment to determine Planck's constant, a metal surface was irradiated with light of different wavelengths. The emitted photoelectron energies were measured by applying a stopping potential. The relevant data for the wavelength (λ)( \lambda ) of incident light and the corresponding stopping potential \left({V}_{0}\right)aregivenbelow:<br/><tableborder="1"style="width:100px;height:100px;"><tbody><tr><td>are given below:<br /> <table border="1" style="width: 100px; height: 100px;"> <tbody> <tr> <td>\lambda\left(\mum\right) V0(Volt){V}_{0}\left(Volt\right) 0.3 2.0 0.4 1.0 0.5 0.4
Given that c=3×108ms−1ande=1.6×10−19C,c = 3 \times {10}^{8}m{s}^{- 1}ande = 1.6 \times {10}^{- 19}C, Planck's constant (in units of J s) found from such an experiment is :

Options

  1. A6.0×10−346.0 \times {10}^{- 34}
  2. B6.4×10−346.4 \times {10}^{- 34}
  3. C6.6×10−346.6 \times {10}^{- 34}
  4. D6.8×10−346.8 \times {10}^{- 34}

Correct answer

B. 6.4×10−346.4 \times {10}^{- 34}

Step-by-step solution

K{E}_\max = \dfrac{hC}{\lambda} - ϕ

e(V0)=hCλ−ϕe\left({V}_{0}\right) = \dfrac{hC}{\lambda} - ϕ
1.6×10−19×2=h×3×1083000×10−10−ϕ1.6 \times {10}^{- 19} \times 2 = \dfrac{h \times 3 \times {10}^{8}}{3000 \times {10}^{- 10}} - ϕ .....(i)
1.6×10−19×1=h×3×1084000×10−10−ϕ1.6 \times {10}^{- 19} \times 1 = \dfrac{h \times 3 \times {10}^{8}}{4000 \times {10}^{- 10}} - ϕ .......(ii)
From (ii) ϕ=h×3×1084000×10−10−1.6×10−19ϕ = \dfrac{h \times 3 \times {10}^{8}}{4000 \times {10}^{- 10}} - 1.6 \times {10}^{- 19}

Using value of ϕϕ in equation (i), we get
1.6×10−19×2=h×3×1083000×10−10−h×3×1084000×10−10+1.6×10−191.6 \times {10}^{- 19} \times 2 = \dfrac{h \times 3 \times {10}^{8}}{3000 \times {10}^{- 10}} - \dfrac{h \times 3 \times {10}^{8}}{4000 \times {10}^{- 10}} + 1.6 \times {10}^{- 19}
1.6×10−19=h×3×10810−7(13−14)=h×3×10810−7[4−312]1.6 \times {10}^{- 19} = \dfrac{h \times 3 \times {10}^{8}}{{10}^{- 7}}\left(\dfrac{1}{3} - \dfrac{1}{4}\right) = \dfrac{h \times 3 \times {10}^{8}}{{10}^{- 7}}\left[\dfrac{4 - 3}{12}\right]
1.6×10−19=h×3×10810−7×1121.6 \times {10}^{- 19} = \dfrac{h \times 3 \times {10}^{8}}{{10}^{- 7}} \times \dfrac{1}{12}
1.6×4×10−19×10−7108=h1.6 \times 4 \times \dfrac{{10}^{- 19} \times {10}^{- 7}}{{10}^{8}} = h
6.4×10−34Js=h6.4 \times {10}^{- 34}Js = h

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