enEnglishhiहिन्दी
JEE Mains · Physics · STD 12 - 11. Dual nature of radiation and matter
When photons of wavelength \(\lambda _1\) are incident on an isolated sphere, the corresponding stopping potential is found to be \(V.\) When photons of wavelength \(\lambda _2\) are used, the corresponding stopping potential was thrice that of the above value . If light of wavelength \(\lambda _3\) is used then find the stopping potential for this case
- A \(\frac{{hc}}{e}\left[ {\frac{1}{{{\lambda _3}}} + \frac{1}{{{\lambda _2}}} - \frac{1}{{{\lambda _1}}}} \right]\)
- B \(\frac{{hc}}{e}\left[ {\frac{1}{{{\lambda _3}}} + \frac{1}{{{2\lambda _2}}} - \frac{1}{{{\lambda _1}}}} \right]\)
- C \(\frac{{hc}}{e}\left[ {\frac{1}{{{\lambda _3}}} - \frac{1}{{{\lambda _2}}} - \frac{1}{{{\lambda _1}}}} \right]\)
- D \(\frac{{hc}}{e}\left[ {\frac{1}{{{\lambda _3}}} + \frac{1}{{{2\lambda _2}}} - \frac{3}{{{2\lambda _1}}}} \right]\)
Answer & Solution
Correct Answer
(D) \(\frac{{hc}}{e}\left[ {\frac{1}{{{\lambda _3}}} + \frac{1}{{{2\lambda _2}}} - \frac{3}{{{2\lambda _1}}}} \right]\)
Step-by-step Solution
Detailed explanation
From Einstein's photoelectric equation, we have \(\frac{h c}{\lambda_{1}}=\frac{h c}{\lambda_{0}}+e V\) ..... \((1)\) \(\frac{\mathrm{hc}}{\lambda_{2}}=\frac{\mathrm{hc}}{\lambda_{0}}+3 \mathrm{eV}\) ..... \((2)\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- A body of mass \(1 kg\) begins to move under the action of a time dependent force \(\vec{F}=\left(t \hat{i}+3 t^2 \hat{ j }\right) N\). where \(\hat{i}\) and \(\hat{j}\) are the unit vectors along \(x\) and \(y\) axis. The 10.Power developed by above force, at the time \(t=2 s\). will be \(..............W\).JEE Mains 2023 Medium
- A square loop of side \(2\, a ,\) and carrying current I, is kept in \(XZ\) plane with its centre at origin. A long wire carrying the same current \(I\) is placed parallel to the \(z-\)axis and passing through the point \((0, b, 0),(b>>a)\). The magnitude of the torque on the loop about \(z-\)axis is given by:JEE Mains 2020 Hard
- The diameter of an air bubble which was initially \(2\,mm\), rises steadily through a solution of density \(1750\,kg\,m\,m ^{-3}\) at the rate of \(0.35\,cms ^{-1}\). The coefficient of viscosity of the solution is poise (in nearest integer). (the density of air is negligible).JEE Mains 2022 Medium
- A wedge \(Y\) with mass of \(10\) kg and all frictionless surfaces and the inclined surface making \(37°\) with horizontal. A block \(X\) with mass \(2\) kg is placed at the highest point of the wedge as shown in figure is at rest. At \(t = 0\) wedge \((Y)\) is pulled toward right with constant force \((f)\) of \(24\) N. Taking the block \(X\) at rest at \(t = 0\), the time taken by it to slide down \(8.8\) m on the slope, while \(Y\) is on the move, is _____ s.
(take \(\tan(37°) = 3/4\) and \(g = 10\) m/s\(^2\))
JEE Mains 2026 Hard - A body of mass \({M}\) moving at speed \({V}_{0}\) collides elastically with a mass \('m'\) at rest. After the collision, the two masses move at angles \(\theta_{1}\) and \(\theta_{2}\) with respect to the initial direction of motion of the body of mass \({M}\). The largest possible value of the ratio \({M} / {m}\), for which the angles \(\theta_{1}\) and \(\theta_{2}\) will be equal, is :JEE Mains 2021 Hard
- Consider a long straight wire of a circular cross-section (radius a) carrying a steady current I. The current is uniformly distributed across this cross-section. The distances from the centre of the wire's cross-section at which the magnetic field [inside the wire, outside the wire] is half of the maximum possible magnetic field, any where due to the wire, will beJEE Mains 2025 Medium
More PYQs from JEE Mains
- If \(\int\left(\frac{1}{x}+\frac{1}{x^3}\right) \left(\sqrt[23]{3 x^{-24}+x^{-26}}\right) d x \) \( =-\frac{\alpha}{3(\alpha+1)}\left(3 x^\beta+x^\gamma\right)^{\frac{\alpha+1}{\alpha}}+C, x \gt 0,\) \((\alpha, \beta, \gamma \in Z)\), where \(C\) is the constant of integration, then \(\alpha+\beta+\gamma\) is equal to ________ .JEE Mains 2025 Medium
- The minimum frequency of photon required to break a particle of mass 15.348 amu into 4\( \alpha \) particles is __________ kHz.
[mass of He nucleus = 4.002 amu,
\(1 amu =1.66 \times 10^{-27} kg, h =6.6 \times 10^{-34} J . s\) and \(c =\) \(\left.3 \times 10^8 m / s \right]\)JEE Mains 2026 Medium - A metal sample carrying a current along \(X-\) axis with density \(J_x\) is subjected to a magnetic field \(B_z\) ( along \(z-\) axis ). The electric field \(E_y\) developed along \(Y-\) axis is directly proportional io \(J_x\) as well as \(B_z\) . The constant of proportionality has \(SI\, unit\).JEE Mains 2013 Medium
- A three coulomb charge moves from the point \((0, -2, -5)\) to the point \((5, 1, 2)\) in an electric field expressed as \(\vec{E} = 2x\hat{i} + 3y^2\hat{j} + 4\hat{k}\) N/C. The work done in moving the charge is _______ J.JEE Mains 2026 Hard
- A \(9\, V\) battery with internal resistance of \(0.5\,\Omega \) is connected across an infinite network as shown in the figure. All ammeters \(A_1 , A_2, A_3\) and voltmeter \(V\) are ideal. Choose correct statement
JEE Mains 2017 Hard - A solid sphere of mass ' \(m\) ' and radius ' \(r\) ' is allowed to roll without slipping from the highest point of an inclined plane of length ' \(L\) ' and makes an angle \(30^{\circ}\) with the horizontal. The speed of the particle at the bottom of the plane is \(v_1\). If the angle of inclination is increased to \(45^{\circ}\) while keeping \(L\) constant. Then the new speed of the sphere at the bottom of the plane is \(v_2\). The ratio \(v_1^2: v_2^2\) is:JEE Mains 2025 Hard