Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Advanced 2006
Exam
JEE Advanced
Year
2006
Subject
Physics
Chapter
Dual Nature of Matter

JEE Advanced 2006 · Physics · Dual Nature of Matter

The graph between 1 / λ and stopping potential (V) of three metals...

The graph between 1/λ1 / \lambda and stopping potential (V)(V) of three metals having work function ϕ1,ϕ2\phi_1, \phi_2 and ϕ3\phi_3 in an experiment of photoelectric effect is plotted as shown in the figure. Which of the following statement(s) is/are correct? [Here λ\lambda is the wavelength of the incident ray]. The graph between 1 / λ and stopping potential (V) of three metals having work function φ_1, φ_2 and φ_3 in an

Options

  1. ARatio of work functions ϕ1:ϕ2:ϕ3=1:2:4\phi_1: \phi_2: \phi_3=1: 2: 4.
  2. BRatio of work functions ϕ1:ϕ2:ϕ3=4:2:1\phi_1: \phi_2: \phi_3=4: 2: 1.
  3. Ctan⁡θ\tan \theta is directly proportional to hc/eh c / e, where hh is Planck's constant and cc is the speed of light.
  4. DThe violet colour light can eject photoelectrons from metals 2 and 3.

Correct answer

A. Ratio of work functions ϕ1:ϕ2:ϕ3=1:2:4\phi_1: \phi_2: \phi_3=1: 2: 4.

Step-by-step solution

From the relation, eV=hcλ−ϕe V=\frac{h c}{\lambda}-\phi or V=V=\left(\frac{h c}{e}\right)(1λ)−ϕe\left(\frac{1}{\lambda}\right)-\frac{\phi}{e} This is equation of straight line. Slope is tan⁡θ=hce\tan \theta=\frac{h c}{e}ϕ1:ϕ2:ϕ3=hcλ01:hcλ02:hcλ03=1λ01:1λ02:1λ03=1:2:41λ01=0.001nm−1 or  λ01=10000A˚1λ02=0.002nm−1 or λ02=5000A˚1λ03=0.004nm−1 or λ03=25000A˚\begin{aligned} \phi_1: \phi_2: \phi_3 & =\frac{h c}{\lambda_{01}}: \frac{h c}{\lambda_{02}}: \frac{h c}{\lambda_{03}}=\frac{1}{\lambda_{01}}: \frac{1}{\lambda_{02}}: \frac{1}{\lambda_{03}}=1: 2: 4 \\ \frac{1}{\lambda_{01}} & =0.001 \mathrm{ nm}^{-1} \text{\text{ or } } \lambda_{01}=10000 Å \\ \frac{1}{\lambda_{02}} & =0.002 \mathrm{ nm}^{-1} \text{ or } \lambda_{02}=5000 Å \\ \frac{1}{\lambda_{03}} & =0.004 \mathrm{ nm}^{-1} \text{ or } \lambda_{03}=25000 Å \end{aligned}VioletcolourhaswavelengthViolet colour has wavelength4000 Å. So, violet colour can eject photoelectrons from metal-1 and metal-2.
Practice Dual Nature of Matter on Quantrex Academy →

More from Dual Nature of Matter

K_1 and K_2 be the maximum kinetic energies of photoelectrons emitted from a surface of a… JEE Main 2026The de Broglie wavelength for an electron accelerated through the potential difference of… JEE Main 2026Given below are two statements: one is labelled as Assertion (A) and the other is… JEE Main 2026An electron is travelling with a velocity v in free space and when it enters a medium… JEE Main 2026An electron of mass m is moving in an electric field E = -2E_0 i ( E_0 = constant > 0 )… JEE Main 2026Light source having wavelength 331 nm is used to generate photo-electrons whose stopping… JEE Main 2026Match the LIST-I with LIST-II List-I List-II A. Planck's constant I. ML^2T^ -2 B.… JEE Main 2026The de Broglie wavelength associated with an electron accelerated through a potential… JEE Main 2026 Full Dual Nature of Matter list All JEE Advanced PYQs