What is Threshold Wavelength?

S4-SA1-0543

Grade Level:

Class 8

Space Technology, EVs, Climate Change, Biotechnology, HealthTech, Robotics, Chemistry, Physics

Definition

What is it?

Threshold wavelength is the longest possible wavelength of light that can cause electrons to be ejected from a metal surface. If the light has a wavelength longer than this 'threshold,' no electrons will be released, no matter how bright the light is.

Simple Example

Quick Example

Imagine you need to jump over a wall to get into a special garden. The wall is like the 'threshold wavelength'. If you can jump just high enough (wavelength is short enough), you get in. If you try to jump, but the wall is too high for your jump (wavelength is too long), you won't get in, even if you try many times.

Worked Example

Step-by-Step

Let's say a special metal needs light with energy of at least 4 x 10^-19 Joules to release an electron.

We know the formula for energy of light (E) is E = hc/lambda, where h is Planck's constant (6.626 x 10^-34 Js), c is the speed of light (3 x 10^8 m/s), and lambda is the wavelength.

---Step 1: We need to find the longest wavelength (threshold wavelength) that provides this minimum energy.

---Step 2: Set the energy E to the minimum required energy: E = 4 x 10^-19 J.

---Step 3: Rearrange the formula to solve for lambda: lambda = hc/E.

---Step 4: Substitute the values: lambda = (6.626 x 10^-34 Js * 3 x 10^8 m/s) / (4 x 10^-19 J).

---Step 5: Calculate the numerator: 6.626 x 3 = 19.878. 10^-34 * 10^8 = 10^-26. So, numerator = 19.878 x 10^-26 Jm.

---Step 6: Divide: lambda = (19.878 x 10^-26 Jm) / (4 x 10^-19 J) = 4.9695 x 10^-7 m.

---Step 7: Convert to nanometers (1 m = 10^9 nm): 4.9695 x 10^-7 m * 10^9 nm/m = 496.95 nm.

Answer: The threshold wavelength for this metal is approximately 497 nanometers.

Why It Matters

Understanding threshold wavelength is crucial for developing technologies like solar panels, which convert sunlight into electricity. It helps engineers design more efficient sensors for space technology and medical devices. This concept is vital for careers in renewable energy, photonics, and materials science.

Common Mistakes

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

MISTAKE: Confusing threshold wavelength with threshold frequency. | CORRECTION: Threshold wavelength is the maximum wavelength, while threshold frequency is the minimum frequency required. They are inversely related.

MISTAKE: Believing that all metals have the same threshold wavelength. | CORRECTION: Each metal has a unique threshold wavelength because the electrons are held with different strengths in different materials.

Practice Questions

Try It Yourself

QUESTION: If a metal has a threshold wavelength of 500 nm, will light with a wavelength of 450 nm cause electrons to be ejected? | ANSWER: Yes, because 450 nm is shorter than 500 nm.

QUESTION: A metal needs at least 3.5 x 10^-19 J of energy to release an electron. Calculate its threshold wavelength (h = 6.626 x 10^-34 Js, c = 3 x 10^8 m/s). | ANSWER: lambda = hc/E = (6.626 x 10^-34 * 3 x 10^8) / (3.5 x 10^-19) = 5.679 x 10^-7 m or 568 nm.

QUESTION: Light with a wavelength of 600 nm hits a metal, but no electrons are released. What can you say about the metal's threshold wavelength? If the light's wavelength is changed to 400 nm and electrons are released, what is the range for the threshold wavelength? | ANSWER: The metal's threshold wavelength must be less than 600 nm. If 400 nm light works, then the threshold wavelength is between 400 nm and 600 nm (exclusive of 600 nm, inclusive of 400 nm if 400 nm is the exact threshold).

MCQ

Quick Quiz

Which of the following statements about threshold wavelength is correct?

It is the shortest wavelength of light that can eject electrons.

It is the longest wavelength of light that can eject electrons.

It depends only on the brightness of the light.

It is the same for all types of metals.

The Correct Answer Is:

Threshold wavelength is the maximum wavelength of light that has enough energy to release electrons. Wavelengths longer than this do not have enough energy, regardless of brightness.

Real World Connection

In the Real World

You see threshold wavelength in action every day in solar calculators or the solar panels on rooftops in Indian cities. These devices use materials that are carefully chosen so their threshold wavelength allows them to absorb visible light from the sun and convert it into electricity, powering our homes and gadgets.

Key Vocabulary

Key Terms

WAVELENGTH: The distance between two consecutive crests or troughs of a wave | ELECTRON: A tiny, negatively charged particle that orbits the nucleus of an atom | PHOTOELECTRIC EFFECT: The phenomenon where electrons are ejected from a metal surface when light shines on it | ENERGY: The capacity to do work or produce heat.

What's Next

What to Learn Next

Great job learning about threshold wavelength! Next, you should explore 'Photoelectric Effect' and 'Work Function'. These concepts build directly on what you've learned and will help you understand how solar cells and other light-sensitive devices truly work.