Question 58: Dual Nature of Matter and Radiation

Question

The graph between $\frac{1}{\lambda}$ and stopping potential (V) of three metals having work functions $\phi_1, \phi_2$, and $\phi_3$ in an experiment of photoelectric effect is plotted as shown in the figure. Which of the following statement(s) is/are correct? (Here, $\lambda$ is the wavelength of the incident ray).

Accepted Answer

The energy of incident photon $\frac{h c}{\lambda}$ is equal to the sum of minimum energy required to emit the photoelectron (work function) and kinetic energy K of the ejected photoelectron.
The stopping potential V converts the kinetic energy K of ejected photoelectron into potential energy eV , there by stopping its motion.
Thus, $\frac{h c}{\lambda}=\phi+\mathrm{K}=\phi+\mathrm{eV}$
$$ \Rightarrow \frac{h c}{\lambda}-\phi=\mathrm{eV} . $$
i.e., $\mathrm{V}=\frac{h c}{e} \cdot \frac{1}{\lambda}-\frac{\phi}{e} \quad$ Slope, $m=	an 	heta=\frac{h c}{e}$
(on comparing with $y=m x-c$ )
At $\mathrm{V}=0, \phi=\frac{h c}{\lambda}$ which gives
$$ \phi_1=0.001 h c, \phi_2=0.002 h c, \phi_3=0.004 h c, $$
(For metal 1)           (metal 2)              (metal 3)
Thus, $\phi_1: \phi_2: \phi_3:: 1: 2: 4$.
Also, $\phi=\frac{h c}{\lambda_0}$, where $\lambda_0$ is threshold wavelength,
$	herefore$ The wavelength corresponding to $\phi_1, \phi_2, \lambda_3$ are
$$ \begin{aligned} & \lambda_1=\frac{1}{0.001}=1000 \mathrm{~nm} \ & \lambda_2=\frac{1}{0.002}=500 \mathrm{~nm} \ & \lambda_3=\frac{1}{0.004}=250 \mathrm{~nm} \end{aligned} $$
The wavelength of violet colour light is close to 400 nm , which is more than the threshold wavelength for metal 3 . Thus violet light can eject photoelectrons from from metal 2 but not from metal 3 .

Answer

Ratio of work functions $\phi_1: \phi_2: \phi_3 =1: 2: 4$.

Answer

Ratio of work functional $\phi_1: \phi_2: \phi_3 =4: 2: 1$.

Answer

$	an 	heta$ is directly proportional to $\frac{h c}{e}$, where $h$ is Planck's constant and $c$ is the speed of light.

Answer

The violet colour light can eject photoelectrons from metals 2 and 3 .

Dual Nature of Matter and Radiation

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