Dual Nature of Matter

JEE Main level, single correct, medium

190 of 200

Question 190 of 200

This question has Statement −1-1 and Statement −2-2. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement-1 : A metallic surface is irradiated by a monochromatic light of frequency
v>v0v\gt v_0 (the threshold frequency). The maximum kinetic energy and the stopping potential are Kmax⁡\mathrm{K}_{\max } and V0\mathrm{V}_0 respectively. If the frequency incident on the surface doubled, both the Kmax⁡\mathrm{K}_{\max } and V0\mathrm{V}_0 are also doubled.
Statement-2 : The maximum kinetic energy and the stopping potential of photoelectrons emitted from a surface are linearly dependent on the frequency of incident light.

Show answer and solution

Answer: (C) Statement-1 is false, Statement-2 is true.

KEmax⁡=hu−hu0hu−hu=e×ΔvV0=hue−hv0e\begin{aligned} & \mathrm{KE}_{\max }=\mathrm{hu}-\mathrm{hu}_0 \\ & \mathrm{hu}-\mathrm{hu}=\mathrm{e} \times \Delta \mathrm{v} \\ & \mathrm{V}_0=\frac{\mathrm{hu}}{\mathrm{e}}-\frac{\mathrm{hv_{0 }}}{\mathrm{e}} \end{aligned}
'
vv ' is doubled
KEmax⁡=2hu−hu0 V0′=(ΔV)′=2hue−hu0e\begin{aligned} & \mathrm{KE}_{\max }=2 \mathrm{hu}-\mathrm{hu}_0 \\ & \mathrm{~V}_0^{\prime}=(\Delta \mathrm{V})^{\prime}=\frac{2 \mathrm{hu}}{\mathrm{e}}-\frac{h \mathrm{u}_0}{\mathrm{e}} \end{aligned}
KEmax⁡KEmax⁡\frac{\mathrm{KE}_{\max }}{\mathrm{KE}_{\max }} may not be equal to 2
⇒V0′V0\Rightarrow \frac{\mathrm{V}_0^{\prime}}{\mathrm{V}_0} may not equal to 2
KEmax⁡=hu−hv0\mathrm{KE} \max =\mathrm{hu}-\mathrm{hv}_0
V=hve−h h0e\mathrm{V}=\frac{h \mathrm{v}}{\mathrm{e}}-\frac{h \mathrm{~h}_0}{\mathrm{e}}

JEE Main question paper PDF

Open a shift to read the full paper on this page, or download it.

JEE Main 2025 Apr 2 Shift 1 question paper

Open Download PDF

Opening paper…

Explain it as a whiteboard videoStep-by-step, in Hinglish or English. Your first video needs no login.Solved it on paper but got it wrong?Upload a photo of your working. Mistake Doctor marks the exact line that broke.
See it move: Photoelectric effect and matter waves simulationDrag the sliders and watch the numbers in this question change.Revise Modern Physics firstFormula sheet, solved examples and the traps students fall into.

More Physics practice

JEE Main Physics practice question on Dual Nature of Matter (Photoelectric Effect), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.