What is Threshold Wavelength? | Simple Explanation for Class 12

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What is the Threshold Wavelength for Photoelectric Effect?

Grade Level:

Class 12

AI/ML, Physics, Biotechnology, FinTech, EVs, Space Technology, Climate Science, Blockchain, Medicine, Engineering, Law, Economics

Definition

What is it?

The threshold wavelength is the maximum wavelength of light that can cause electrons to be ejected from a metal surface in the photoelectric effect. If the light's wavelength is longer than this threshold, no electrons will be emitted, no matter how bright the light is.

Simple Example

Quick Example

Imagine you need a special key (light) to open a lock (metal surface) and get a prize (electron). This lock only opens with keys that are 'short enough' (small wavelength). If your key is too long (wavelength is too high), it won't work, even if you have many such long keys. The threshold wavelength is the longest key that can still open the lock.

Worked Example

Step-by-Step

Let's find the threshold wavelength for a metal with a work function of 2.1 eV. (Given: h = 6.626 x 10^-34 J.s, c = 3 x 10^8 m/s, 1 eV = 1.6 x 10^-19 J)

Step 1: Convert the work function from eV to Joules.
Work function (Φ) = 2.1 eV * 1.6 x 10^-19 J/eV = 3.36 x 10^-19 J

--- Step 2: Recall the formula relating work function, Planck's constant, speed of light, and threshold wavelength.
Φ = hc / λ₀ (where λ₀ is the threshold wavelength)

--- Step 3: Rearrange the formula to solve for threshold wavelength.
λ₀ = hc / Φ

--- Step 4: Plug in the values and calculate.
λ₀ = (6.626 x 10^-34 J.s * 3 x 10^8 m/s) / (3.36 x 10^-19 J)

--- Step 5: Calculate the numerator.
Numerator = 19.878 x 10^-26 J.m

--- Step 6: Perform the final division.
λ₀ = 19.878 x 10^-26 / 3.36 x 10^-19 m = 5.916 x 10^-7 m

--- Step 7: Convert to nanometers (optional, but common for wavelengths).
λ₀ = 591.6 nm

Answer: The threshold wavelength is approximately 591.6 nm.

Why It Matters

Understanding threshold wavelength is crucial for designing solar cells that convert sunlight into electricity, powering everything from your calculator to ISRO's satellites. It's also vital in sensors for AI/ML systems and in medical imaging devices, creating exciting career paths in renewable energy and advanced technology.

Common Mistakes

MISTAKE: Thinking that any light, if bright enough, will cause electron emission. | CORRECTION: Only light with a wavelength shorter than or equal to the threshold wavelength (or frequency higher than threshold frequency) can cause emission, regardless of intensity.

MISTAKE: Confusing threshold wavelength with work function. | CORRECTION: Work function is the minimum energy required to eject an electron, while threshold wavelength is the maximum wavelength of light corresponding to that minimum energy.

MISTAKE: Using the wrong units in calculations, especially for energy (eV vs. Joules) or wavelength (nm vs. m). | CORRECTION: Always convert all values to standard SI units (Joules, meters, seconds) before calculation, or ensure consistency in units throughout the problem.

Practice Questions

Try It Yourself

QUESTION: A metal has a threshold wavelength of 600 nm. Will light with a wavelength of 650 nm cause photoelectric emission? | ANSWER: No, because 650 nm is longer than the threshold wavelength.

QUESTION: If the work function of a metal is 2.5 eV, calculate its threshold wavelength. (Use h = 6.6 x 10^-34 J.s, c = 3 x 10^8 m/s, 1 eV = 1.6 x 10^-19 J) | ANSWER: λ₀ = (6.6 x 10^-34 * 3 x 10^8) / (2.5 * 1.6 x 10^-19) = 4.95 x 10^-7 m or 495 nm.

QUESTION: A specific metal requires light of at least 500 nm to eject electrons. If light of 400 nm hits the surface, will electrons be emitted? If yes, will they have higher kinetic energy than if 450 nm light was used? Explain. | ANSWER: Yes, electrons will be emitted because 400 nm is shorter than 500 nm. Yes, they will have higher kinetic energy. Shorter wavelength means higher energy per photon, and since the work function is constant, the excess energy goes into the kinetic energy of the ejected electrons.

MCQ

Quick Quiz

Which of the following statements about threshold wavelength (λ₀) is correct?

It is the minimum wavelength required for photoelectric emission.

It is the maximum wavelength required for photoelectric emission.

It depends on the intensity of incident light.

It is the wavelength at which electrons gain maximum kinetic energy.

The Correct Answer Is:

The threshold wavelength is the longest possible wavelength of light that can still eject an electron. Any wavelength longer than this will not cause emission. It does not depend on intensity and is not related to maximum kinetic energy directly.

Real World Connection

In the Real World

You see the threshold wavelength in action every day in solar panels on rooftops or streetlights. These panels are made of materials like silicon, which have a specific threshold wavelength. They are designed to absorb sunlight (which has wavelengths shorter than silicon's threshold) to generate electricity, powering homes and charging your mobile phones through solar chargers.

Key Vocabulary

Key Terms

Photoelectric Effect: The emission of electrons when light shines on a material. | Work Function: The minimum energy needed to remove an electron from a metal surface. | Photon: A particle of light, carrying a specific amount of energy. | Wavelength: The distance between two consecutive crests or troughs of a wave.

What's Next

What to Learn Next

Next, you should explore the 'Photoelectric Equation' by Einstein. This equation will help you understand how the energy of incoming light, the work function, and the kinetic energy of emitted electrons are all connected, building directly on your knowledge of threshold wavelength.