Question:
When radiation of wavelength \(\lambda\) is incident on a metallic surface, the stopping potential of ejected photoelectrons is \(4.8\ \mathrm{V}\). If the same surface is illuminated by radiation of double the previous wavelength, then the stopping potential becomes \(1.6\ \mathrm{V}\). The threshold wavelength of the metal is :
When radiation of wavelength \(\lambda\) is incident on a metallic surface, the stopping potential of ejected photoelectrons is \(4.8\ \mathrm{V}\). If the same surface is illuminated by radiation of double the previous wavelength, then the stopping potential becomes \(1.6\ \mathrm{V}\). The threshold wavelength of the metal is :
Show Hint
Write Einstein's equation for both wavelengths and subtract to eliminate the work function.
Updated On: Nov 4, 2026
- \(2\lambda\)
- \(4\lambda\)
- \(8\lambda\)
- \(6\lambda\)
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Einstein: \(eV_s = \dfrac{hc}{\lambda} - \phi\).
Case 1: \(4.8e = \dfrac{hc}{\lambda} - \phi\). Case 2: \(1.6e = \dfrac{hc}{2\lambda} - \phi\).
Subtract: \(3.2e = \dfrac{hc}{2\lambda}\) \(\Rightarrow\) \(\dfrac{hc}{\lambda} = 6.4e\).
Then \(\phi = 6.4e - 4.8e = 1.6e\).
Threshold wavelength: \(\lambda_0 = \dfrac{hc}{\phi} = \dfrac{6.4e\,\lambda}{1.6e} = 4\lambda\).
Answer: (2) \(4\lambda\)
Case 1: \(4.8e = \dfrac{hc}{\lambda} - \phi\). Case 2: \(1.6e = \dfrac{hc}{2\lambda} - \phi\).
Subtract: \(3.2e = \dfrac{hc}{2\lambda}\) \(\Rightarrow\) \(\dfrac{hc}{\lambda} = 6.4e\).
Then \(\phi = 6.4e - 4.8e = 1.6e\).
Threshold wavelength: \(\lambda_0 = \dfrac{hc}{\phi} = \dfrac{6.4e\,\lambda}{1.6e} = 4\lambda\).
Answer: (2) \(4\lambda\)
Was this answer helpful?
0
0
Top JEE Main Physics Questions
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88×106 nm-K. Then,
- $I _{ CM }$ is the moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc $I_{A B}$ is it's moment of inertia about an axis $AB$ perpendicular to plane and parallel to axis $CM$ at a distance $\frac{2}{3} R$ from center Where $R$ is the radius of the dise The ratio of $I _{ AB }$ and $I _{ CM }$ is $x: 9$ The value of $x$ is______
- A nucleus disintegrates into two smaller parts, which have their velocities in the ratio $3: 2$ The ratio of their nuclear sizes will be $\left(\frac{x}{3}\right)^{\frac{1}{3}}$ The value of ' $x$ ' is:-
- A particle starts with an initial velocity of 10.0 m/s along x-direction and accelerates uniformly at the rate of 2.0 m/s$^2$. The time taken by the particle to reach the velocity of 60.0 m/s is
View More Questions
Top JEE Main Photoelectric Effect Questions
- If the power of a light source is P and frequency of photons emitted is f. Find number photons emitted in time t.
- In a photoelectric experiment, frequency \(f = 1\).\(5f_0\) (\(f_o\): threshold frequency). If the frequency of light is changed to \(\frac{f}{2}\), then photocurrent becomes (intensity of light has doubled)
- If the work function of a metal is 6.63 eV, then find the threshold frequency for photoelectric effect.
- For the photoelectric effect, the maximum kinetic energy \( E_k \) of the photoelectrons is plotted against the frequency \( \nu \) of the incident photons as shown in figure. The slope of the graph gives
- UV light of 4.13 eV is incident on a photosensitive metal surface having work function 3.13 eV. The maximum kinetic energy of ejected photoelectrons will be
View More Questions
Top JEE Main Questions
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88×106 nm-K. Then,
View More Questions