Question 279: Dual Nature of Matter and Radiation

Question

When photons of energies twice and thrice the work function of a metal are incident on the metal surface one after other, the maximum velocities of the photoelectrons emitted in the two cases are $V_1$ and $V_2$ respectively. The ratio $\mathrm{V}_1: \mathrm{V}_2$ is

Accepted Answer

Step 1: Recall the photoelectric equation
$ K_	ext{max} = E_	ext{photon} - \phi $
where $\phi$ is the work function.
Also,
$ K_	ext{max} = 	frac{1}{2} m v^2. $
Step 2: Case 1
Photon energy $E_1 = 2\phi$.
$ K_1 = E_1 - \phi = 2\phi - \phi = \phi. $
So
$ 	frac{1}{2} m V_1^2 = \phi \;\;\;\Rightarrow V_1 = \sqrt{\frac{2\phi}{m}} $
Step 3: Case 2
Photon energy $E_2 = 3\phi$.
$ K_2 = 3\phi - \phi = 2\phi. $
So
$ 	frac{1}{2} m V_2^2 = 2\phi \;\;\;\Rightarrow V_2 = \sqrt{\frac{4\phi}{m}} = 2\sqrt{	frac{\phi}{m}}. $
Step 4: Ratio
$ \frac{V_1}{V_2} = \frac{\sqrt{2\phi/m}}{2\sqrt{\phi/m}} = \frac{\sqrt{2}}{2} = \frac{1}{\sqrt{2}}. $
So
$ V_1:V_2 \;\;=\;\; 1:\sqrt{2}. $
Ã¢ÂÂ Final Answer:
Option D Ã¢ÂÂ $1:\sqrt{2}$

Answer

$\sqrt{3}: \sqrt{2}$

Answer

$\sqrt{2}: 1$

Answer

$\sqrt{3}: 1$

Answer

$1: \sqrt{2}$

Dual Nature of Matter and Radiation

When photons of energies twice and thrice the work function of a metal are incident on the metal surface one after other, the maximum velocities of the photoelectrons emitted in the two cases are V_1 and V_2 respectively. The ratio \mathrm{V}_1: \mathrm{V}_2 is

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