Question

The incorrect statement among the following is (1) Dimensions of Planek's constant are force \(\times\) time. (2) A photon is a quantum of matter. (3) Photoelectric effect shows particle-like behaviour of light. (4) The best metal to be used for photoemission is caesium.

Short answer

Statement 2 is incorrect.

Step-by-step solution

- Analyze Statement 1

Dimensions of Planck's constant are defined in terms of energy and time: \(h = E \times t\). Since energy \(E\) is force \(F\) times distance \(d\) (i.e., \(E = F \times d\)), when substituting this into the formula for \(h\), we get \(h = F \times d \times t\), not just force \(\times t\). Therefore, this statement is incorrect.

- Analyze Statement 2

A photon is a quantum of electromagnetic radiation, not matter. This implies that statement 2 is incorrect.

- Analyze Statement 3

The photoelectric effect demonstrates the particle-like behaviour of light, where photons cause the emission of electrons from a surface. This is a correct statement.

- Analyze Statement 4

Caesium (Cs) is often used in photoemissive materials due to its low work function, making it efficient for photoemission. This statement is correct.

Key concepts

Planck's constant dimensions

Planck's constant, denoted by the symbol \( h \), is a fundamental constant in quantum mechanics. Its dimensions are often misunderstood.

The correct dimensions of Planck's constant are derived from its relation to energy and time. The formula is \( h = E \times t \), where \( E \) stands for energy and \( t \) stands for time. To delve deeper:

• Energy \( E \) itself is a product of force \( F \) and distance \( d \): \( E = F \times d \).
• So when we substitute \( E \) in the formula for \( h \), we get \( h = F \times d \times t \).

It's crucial to understand that Planck's constant cannot be simplified just as force times time, like it was incorrectly implied in the given exercise statement. Realizing the correct dimensions helps in accurately understanding quantum phenomena and calculations.

Photon Quantum

A photon is a fundamental particle representing a quantum of light or electromagnetic radiation.

Unlike matter particles, photons have zero rest mass and always move at the speed of light in a vacuum. They are considered the smallest unit of light and are responsible for all electromagnetic interactions:

• They carry energy proportional to their frequency.
• The formula for energy of a photon is given by \( E = h \times f \), where \( f \) is the frequency of the photon.

Thus, statement 2 in the exercise is incorrect. A photon is not a quantum of matter but a quantum of electromagnetic radiation.

Particle-like behaviour of light

The photoelectric effect is a phenomenon that demonstrates the particle-like behaviour of light.

In this effect, when light (specifically photons) hits a material, it can eject electrons from the surface of the material. Key points include:

• Only specific frequencies of light can cause photoemission, indicating energy quantization.
• The effect supports the idea that light can act as particles (photons), carrying discrete amounts of energy.
• Higher intensity of light does not increase electron energy, but more photons (higher intensity) mean more electrons emitted.

This observable phenomenon was critical in developing the concept of photons and quantum theory.

Photoemission materials

Materials used for photoemission need to have specific characteristics to be efficient.

Photoemission relies on the material's work function, the minimum energy needed to eject an electron. Cesium is noted for its:

• Low work function, which means it requires less energy for photoemission.
• High photoemissive sensitivity, making it effective for various applications like photodetectors.

Different materials have different work functions, but cesium stands out as commonly used because of these advantageous properties. Understanding these materials helps in designing efficient devices for applications involving the photoelectric effect.