Q.A polythene piece rubbed with wool is found to have a negative charge of 3×10−7C.
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🔒 Start your 14-day free trial to unlock the full solution →Concept understanding — Photoelectric Effect
The Photoelectric Effect: When Light Knocks Electrons Loose
Imagine you're throwing tennis balls at a wall covered in loose pebbles. If you throw hard enough, a pebble might get knocked off. That's the basic picture — but the photoelectric effect is the quantum version of this, and it completely shattered classical physics.
The Intuition
Light is made of tiny packets of energy called photons. Each photon carries a specific amount of energy, determined by its colour (frequency). When a photon hits a metal surface, it can transfer its energy to an electron inside the metal. If that energy is enough, the electron breaks free and flies out.
Think of electrons in a metal like people in a room with a high window. To escape, they need enough energy to reach the window sill. A photon is like a boost — but only if it gives enough energy in one shot. No amount of weak boosts (dim light) will work if each individual boost is too small.
The Precise Statement
Ephoton=hf=ϕ+Kmax
Where:
- Ephoton=hf is the energy of a photon (Planck's constant h=6.63×10−34 J⋅s, f is frequency)
- ϕ is the work function — the minimum energy needed to remove an electron from that metal
- Kmax is the maximum kinetic energy of the ejected electron
What Classical Physics Got Wrong
Before Einstein (1905), physicists thought light was a continuous wave. They expected:
- Brighter light → more energy per electron → faster electrons
- Any colour would eventually eject electrons if you waited long enough
But experiments showed the opposite:
| Observation | Classical Prediction | Actual Result |
|---|---|---|
| Effect of intensity | Brighter light → faster electrons | Brighter light → more electrons, same speed |
| Threshold frequency | None — any light works eventually | Below a certain frequency, no electrons no matter how bright |
| Time delay | Electrons need time to absorb energy | Electrons appear instantly (within 10−9 s) |
The Key Insight
Einstein said: light behaves like a stream of particles (photons), each with energy hf. One photon interacts with one electron. If hf<ϕ, the electron cannot escape — period. If hf>ϕ, the excess energy becomes kinetic energy:
Kmax=hf−ϕ
This is why:
- Increasing intensity (more photons) ejects more electrons, but each electron still gets the same energy per photon — so their speed doesn't change.
- Below threshold frequency, even a trillion photons per second can't help — each one is too weak individually.
The photoelectric effect proved that light is quantized — it comes in discrete packets. This was the birth of quantum mechanics. Einstein won the 1921 Nobel Prize for this, not for relativity.
A Worked Example
Problem: A metal has work function ϕ=2.0 eV. Light of frequency f=6.0×1014 Hz shines on it. Find the maximum kinetic energy of ejected electrons. (h=4.14×10−15 eV⋅s)
Step 1: Photon energy
E=hf=(4.14×10−15)(6.0×1014)=2.48 eV …
Why this formula?
Photoelectric Effect: Why the Key Formulas Hold
The photoelectric effect is a cornerstone of quantum physics. It showed that light behaves as particles (photons) , not just waves. Let's build the reasoning step-by-step.
1. The Core Idea: Energy Conservation
When a photon hits a metal surface, it transfers all its energy to a single electron inside the metal.
- The photon's energy is E=hf, where h is Planck's constant and f is the frequency of light.
- The electron needs a minimum energy to escape the metal — this is called the work function, ϕ.
Why only one electron?
Einstein proposed that light is quantized into discrete packets (photons). A single photon cannot split its energy among multiple electrons — it interacts with one electron at a time.
2. The Photoelectric Equation
If the photon's energy is greater than the work function, the excess energy becomes the electron's kinetic energy after escape:
hf=ϕ+Kmax
Where:
- hf = energy of incident photon
- ϕ = work function (minimum energy to remove electron)
- Kmax = maximum kinetic energy of ejected electron
Why "maximum" kinetic energy?
- Electrons inside the metal have different binding energies.
- Some electrons are near the surface (loosely bound) → get maximum K.
- Others are deeper → lose energy in collisions before escaping → lower K.
3. The Stopping Potential Connection
We measure Kmax using a stopping potential Vs:
Kmax=eVs
Where e is the electron charge. This is because:
- An electric field opposing the electron's motion does work eVs to stop it.
- At the stopping potential, the electron's kinetic energy is exactly balanced by the electric potential energy.
Combining:
hf=ϕ+eVs
This is the Einstein photoelectric equation in its most testable form.
4. Why the Threshold Frequency Exists
From the equation:
hf=ϕ+eVs
If f is too low, hf<ϕ. Then:
- The photon cannot supply enough energy to overcome the work function.
- No electron is ejected, regardless of light intensity.
The threshold frequency f0 is when Kmax=0:
hf0=ϕ⇒f0=hϕ
Why intensity doesn't matter for ejection?
- Intensity = number of photons per second.
- Each photon still has energy hf. If hf<ϕ, even a billion photons won't eject an electron — each photon is individually too weak.
5. Why Kinetic Energy Depends on Frequency, Not Intensity
From Kmax=hf−ϕ:
- Frequency f directly determines Kmax.
- Intensity only affects the number of electrons ejected (more photons → more electrons), not their individual energy.
This was the key experimental contradiction with classical wave theory:
- Classical: Higher intensity = bigger wave amplitude = more energy to electrons.
- Reality: Higher frequency = more energy per electron; intensity only changes current.
6. Summary of Key Relationships …
Concept: Quantisation of Charge — any charge is an integer multiple of the elementary charge e=1.6×10−19C.
- The polythene becomes negatively charged, so it has gained electrons from the wool.
Number of electrons transferred:
Electrons move from wool to polythene.
n=eQ=1.6×10−193×10−7=1.875×1012
- Yes, there is a transfer of mass. Each electron has mass me=9.1×10−31kg. Mass transferred: …
Number of electrons =q/e=1.6×10−193×10−7≈1.9×1012, transferred from wool to polythene; the mass transferred (wool→polythene) is about 1.7×10−18 kg.
- Electrons transferred. The polythene ends up negatively charged, so it has gained electrons; electrons move from wool to polythene. With q=3×10−7 C and e=1.6×10−19 C,
n=eq=1.6×10−193×10−7=1.875×1012 electrons (≈1.9×1012).
- Mass transfer. Yes. Since electrons carry mass, the electrons moving to the polythene carry mass with them, so there is a transfer of mass from wool to polythene. Using me=9.1×10−31 kg, …
Method: Quantisation of Charge
This problem uses the principle of quantisation of charge — any net charge on an object is an integer multiple of the elementary charge e=1.6×10−19C.
Steps
Step 1: Identify the direction of electron transfer
- Polythene becomes negatively charged → it has gained electrons.
- Wool becomes positively charged → it has lost electrons.
- Electrons are transferred from wool to polythene.
Step 2: Use the quantisation formula
The net charge Q on polythene is:
Q=n⋅e
where
- Q=3×10−7C (given)
- e=1.6×10−19C
- n = number of electrons transferred
Step 3: Solve for n
n=eQ=1.6×10−193×10−7
Step 4: Calculate
n=1.875×1012
Step 5: Answer part (a)
Number of electrons transferred = 1.875×1012 electrons, from wool to polythene.
Step 6: Answer part (b) — mass transfer
- Each electron has mass me=9.1×10−31kg.
- Total mass transferred: …
Common Mistakes in Photoelectric / Charge Transfer Problems
Students often confuse this electrostatics problem with the photoelectric effect. Let's clarify: this is a charge transfer (triboelectric) problem, not photoelectric effect. Here are the common mistakes and how to avoid them.
Mistake 1: Confusing the direction of electron transfer
The error: Students think electrons move from polythene to wool because polythene becomes negative.
Why it's wrong:
A negative charge means an excess of electrons. Polythene becomes negative → it gains electrons. Therefore, electrons are transferred from wool to polythene.
How to avoid:
Remember the rule:
- Negative charge = gained electrons
- Positive charge = lost electrons
So here:
- Polythene: negative → gains electrons (from wool)
- Wool: positive → loses electrons (to polythene)
Mistake 2: Using the wrong formula for number of electrons
The error: Using n=eQ but with wrong sign or wrong value of e.
How to avoid:
Use the magnitude of charge:
n=e∣Q∣
where
- Q=3×10−7C
- e=1.6×10−19C (elementary charge)
So:
n=1.6×10−193×10−7=1.875×1012
Answer: 1.875×1012 electrons transferred from wool to polythene.
Mistake 3: Forgetting that electrons have mass
The error: Saying "no mass is transferred because electrons are massless."
Why it's wrong:
Electrons do have mass: me=9.1×10−31kg. Since electrons move, mass is transferred.
How to avoid:
Calculate the mass transferred:
Mass transferred=n×me=(1.875×1012)×(9.1×10−31)
=1.706×10−18kg
Answer: Yes, a tiny mass (≈1.7×10−18kg) is transferred from wool to polythene.
Mistake 4: Confusing this with photoelectric effect
The error: Trying to use E=hf, work function, or threshold frequency.
Why it's wrong: …
- JKBOSE Class 12 Annual Regular Examination 2023Set ANNUAL1 markQ.What is the effect of decrease in wavelength of incident light on the velocity of photoelectrons ?
›Reveal solutionSolution
A shorter wavelength means a higher-energy photon, so by Einstein's photoelectric equation the maximum kinetic energy - and hence the maximum velocity - of the emitted photoelectrons increases.
By Einstein's photoelectric equation, when light of frequency nu (wavelength lambda, with nu = c/lambda) falls on a metal surface of work function phi0, the maximum kinetic energy of an emitted photoelectron is
KE_max = hnu - phi0 = (hc/lambda) - phi0 = (1/2) m v_max^2.
Here h is Planck's constant, c the speed of light, m the electron mass. If the wavelength lambda of the incident light is decreased (keeping the metal, and hence phi0, fixed), the photon energy hc/lambda increases. Since phi0 is a fixed property of the metal, KE_max = (hc/lambda) - phi0 increases as lambda decreases.
Because KE_max = (1/2) m v_max^2, an increase in KE_max means the maximum velocity v_max of the emitted photoelectrons also increases:
v_max = sqrt[2(hc/lambda - phi0)/m].
…
- JKBOSE Class 12 Annual Regular Examination 2022Set SZ1 markQ.Define threshold frequency.
›Reveal solutionSolution
Threshold frequency is the minimum light frequency needed to just eject an electron from a metal surface, related to the work function by W0=hν0.
When light of a certain frequency falls on a metal surface, photoelectrons are emitted only if the frequency of the incident light is high enough to supply at least the minimum energy needed to free an electron from the metal (the work function W0).
The threshold frequency, denoted ν0, is defined as the minimum frequency of incident radiation which can just cause photoelectric emission from a given metal surface, with zero kinetic energy given to the emitted electron. For frequencies below ν0, no photoelectrons are emitted at all, regardless of how intense (bright) the incident light is — only the number of electrons emitted increases with intensity, not whether emission occurs.
…
- JKBOSE Class 12 Annual Regular Examination 2021Set SZ1 markQ.Define Work Function.
›Reveal solutionSolution
Work function is the minimum binding energy that must be supplied to free the most loosely bound electron from a metal surface.
In a metal, free electrons are held inside by the attractive forces of positive ions; energy is needed to pull an electron out through the surface.
The work function ϕ0 of a metal is defined as the minimum energy required to just liberate an electron from the metal surface, so that it can escape with zero kinetic energy.
It is related to the threshold frequency ν0 (the minimum frequency of incident light that can cause photoemission) by
ϕ0=hu0=λ0hc
where h is Planck's constant and λ0 is the threshold wavelength.
…
- JKBOSE Class 12 Annual Regular Examination 2018Set ANNUAL1 markMCQQ.Work function is measured in :(a) Electrovolt(b) Volt(c) Joul/sec(d) Watt
›Reveal solutionSolution
Work function is an energy, and by convention is expressed in electronvolts because joules would be inconveniently small numbers.
Work function (ϕ0) is the minimum energy required to just liberate an electron from the surface of a metal (with zero kinetic energy). Being an energy, its SI unit is the joule, but because typical work function values are extremely small in joules (of order 10−19 J), it is conventionally expressed in electronvolts (eV), where 1 eV=1.6×10−19 J — a far more convenient scale (typ …
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