Question

Which of the following statement is correct? (1) The kinetic energy of photoclectrons increases lincarly with wavelength of the light. (2) Photoclectric effect can be explained based on corpuscular nature of light. (3) Einstein was awarded Nobel Prize in physies in 1921 for his theory of relativity. (4) The ratio of energy to frequency of electromagnetic radiation is called Rydberg's constant.

Short answer

Statement (2) is correct.

Step-by-step solution

- Understanding Kinetic Energy and Wavelength

Examine statement (1). According to the photoelectric effect, the kinetic energy of photoelectrons depends on the frequency of the light, not its wavelength. Hence, this statement is incorrect.

- Corpuscular Nature of Light

Look at statement (2). The photoelectric effect is indeed explained by the corpuscular (particle) nature of light, as photons are particles of light that can impart energy to electrons. This statement is correct.

- Nobel Prize Facts

Consider statement (3). Einstein received the Nobel Prize in Physics in 1921 for his explanation of the photoelectric effect, not for his theory of relativity. Therefore, this statement is incorrect.

- Energy to Frequency Ratio

Evaluate statement (4). The ratio of energy to frequency of electromagnetic radiation gives us Planck's constant, not Rydberg's constant. This statement is incorrect.

Key concepts

Kinetic Energy and Wavelength

The kinetic energy (KE) of photoelectrons is key in understanding the photoelectric effect. According to Einstein's photoelectric equation, the kinetic energy of photoelectrons is given by \[ KE = hu - \phi \] where \( h \) is Planck's constant, \( u \) is the frequency of the incident light, and \( \phi \) is the work function of the material. This relation shows that the kinetic energy depends on the frequency of the light, not its wavelength. Since frequency and wavelength are inversely related, \(u = \frac {c} {\lambda} \) where \( c \) is the speed of light and \(\lambda \) is the wavelength. The kinetic energy decreases as wavelength increases, emphasizing that wavelength indirectly affects KE but not linearly.

Corpuscular Nature of Light

The concept that light can behave as particles is known as the corpuscular nature of light. Einstein's explanation of the photoelectric effect revolutionized this understanding. He proposed that light consists of quanta, or photons, each carrying discrete amounts of energy given by \( E = hu \). When these photons hit a material, they transfer their energy to electrons, causing them to be ejected if the energy exceeds the material's work function. This particle-like behavior of light successfully explained the photoelectric effect, confirming that light isn't purely a wave but also has particle properties.

Einstein's Nobel Prize

Albert Einstein was awarded the Nobel Prize in Physics in 1921. Interestingly, it wasn't for his famous theory of relativity but for his explanation of the photoelectric effect. Einstein's work provided concrete evidence for the quantum theory of light, validating the concept of photons. His work played a crucial role in developing quantum mechanics, impacting various technological advancements like photovoltaics and photoelectric sensors.

Planck's Constant

One of the fundamental constants in quantum mechanics is Planck's constant (\( h \)). This constant characterizes the relationship between the energy (\( E \)) of a photon and its frequency ( \( u \)), defined by the equation \( E = hu \). Planck's constant has a value of approximately \( 6.626 \times 10^{-34} \). This relation indicates that the energy of light is quantized and comes in discrete packets. Planck's constant is pivotal in understanding the quantum nature of light and other phenomena in modern physics, serving as a bridge between the quantum and classical worlds.