The Photoelectric Effect - Practice Questions & MCQ

Photoelectric effect-

The phenomea of Photoelectric effect was first introduced by Wilhelm Ludwig Franz Hallwachs in 1887 and its experimental verification was confirmed by Heinrich Rudolf Hertz. They observed that when a metallic surface is irradiated by monochromatic light of proper frequency, electrons are emitted from it. This phenomena of ejection of electron is called the Photoelectric effect. 

The photoelectric effect is the process that involves the release or rejection of electrons from the surface of materials (this material is generally a metal) when light falls on them. This concept thatmakes us comfortable to understand quantum  nature of electron and light. 

The electrons ejected during photoelectric effect were called as photoelectrons.There is one condition for photoelectric effect which is very much important that for photoemission to take place, energy of incident light photons should be greater than or equal to the work function of the metal.

Work function $(\phi)$ is defined as the minimum quantity of energy which is required to remove an electron to infinity from the surface of a given solid, usually metal.
Now on the basis of work function $(\phi)$ we can define two related quantity which are Threshold frequency and Threshold wavelength. Now as we know that the energy is of photon is given by -

$
E=h \nu=\frac{h c}{\lambda}
$

Now the frequency corresponding to the energy equals to work function is called Threshold frequency and similarly the wavelength corresponding to the work function is Threshold wavelength.

$
\phi=h \nu_{t h} \quad \nu_{t h}=\frac{\phi}{h}
$

Similarly $\phi=\frac{h c}{\lambda_{t h}} \quad \lambda_{t h}=\frac{h c}{\phi}$

Now, let us understand with experiment which was performed during Heinrich Rudolf Hertz. For this let us consider the given set-up-

In this experiment set-up, an evacuated glass tube is there. Two zinc plates C and A are enclosed. Plates A acts as anode and C acts as a photosensitive plate. Two plates are connected to a battery and ammeter as shown. If the radiation is incident on the plate C through a quartz window, electrons are ejected out of plate and current flows in the circuit this is known as photocurrent. Plate A can be maintained at desired potential (+ve or – ve) with respect to plate C. 

Applications of Photoelectric Effect -

• This phenomena is used to generate electricity in Solar Panels. 
• We come across many sensor in our day to day life. Few sensors are also working in Photoelectric effect.
• It is also used in digital cameras because they have photoelectric sensor.

Note - 

• In case of Threshold frequency - If incident frequency $v<\nu_0$. No photoelectron emission. The minimum frequency of incident radiation to eject electron is threshold frequency ( $\nu_0$ )
  - In case of Threshold Wavelength - If $\lambda>\lambda_0$ No photoelectron emission. The maximum wave length of incident raditaion required to eject the electron is Threshold Wavelength $\left(\lambda_0\right)$
  - Work function
  $h=$ Planck's constant
  $\nu_0=$ thr eshold frequency
  Energy used to overcome the surface barrier and come out of metal surface.

  $
  \phi=h \nu_0
  $

  - Kinetic Energy of Photo eletrons
  $m \rightarrow$ mass of photoelectron
  Remaining part of the energy is used in gaining a velocity $v$ to the emitted photoelectron

  $
  k_{\max }=\frac{1}{2} m v_{\max }^2
  $
   

• Conservation of energy

  

  $
  \begin{aligned}
  & h \nu=\phi_0+\frac{1}{2} m v_{\max }^2 \\
  & h \nu=h \nu_0+\frac{1}{2} m v_{\max }^2
  \end{aligned}
  $

  
  $
  h\left(\nu-\nu_0\right)=\frac{1}{2} m v_{\max }^2
  $

  where, $h-$ Planck's constant, $\nu-$ Frequency, $\nu_0$-threshold frequency, $\phi_0-$ work function

Graphs related to Photoelectric effect -

Before giving the variation in the graph we should define some important terminologies which are used while plotting the graph.

1. Stopping potential-

The negative potential of the collector plate at which the photoelectric current becomes zero is called stopping potential or cut-off potential. Stopping potential is that value of retarding potential difference between two plates which is just sufficient to stop the most energetic photoelectrons emitted. It is denoted by  "".

We need to equate maximum kinetic energy Kmax of the photo-electron (having charge e) to the stopping potential V_o

We know that,
Electric potential energy=Potential Difference $\times$ Charge
So,

$$
\begin{aligned}
& U=V_0 \times Q \\
& U=K_{\max } \\
& \therefore\left|V_0 \times e\right|=K_{\max } \\
& \Rightarrow K_{\max }=\left|e V_0\right|
\end{aligned}
$$

By using previous concept, we can write that -

$$
h \nu=h \nu_o+K \cdot E_{\cdot(\max )}
$$

Now since K.E. $\max =\mathrm{eV}_0$, So we can write that -

$$
\begin{aligned}
& \mathrm{eV}_{\mathrm{s}}=\mathrm{h}\left(\nu-\nu_{\mathrm{o}}\right) \\
& \text { or } \\
& \mathrm{V}_{\mathrm{s}}=\frac{\mathrm{h}}{\mathrm{e}}\left(\nu-\nu_{\mathrm{o}}\right)
\end{aligned}
$$
 

The above graph shows the variation between the stopping potential and frequency.

2. Saturation current - 

The photoelectric current attains a saturation value and does not increase further for any increase in the positive potential. It means that this photoelectric current is the saturation current even we are increasing the value of the positive potential.

Now let us discuss the variation one by one in detail -

1.  Variation of photocurrent with intensity - 

2. Variation of photoelectric current with potential and intensity

3. Effects of frequency of incident light on the stopping potential -

4. Variation of Kinetic energy with frequency