Question

What new idea about light did Einstein use to explain the photoelectric effect? Why does the photoelectric effect exhibit a threshold frequency but not a time lag?

Short answer

Einstein proposed the photon theory, stating that light is composed of particles called photons each with energy proportional to its frequency. The photoelectric effect exhibits a threshold frequency because photons must have enough energy to dislodge electrons, and there is no time lag because this energy transfer occurs instantaneously.

Step-by-step solution

Introduction

The photoelectric effect is the emission of electrons from a metal surface when light shines on it. Traditional wave theories of light failed to explain certain characteristics of this phenomenon, particularly the threshold frequency and the absence of a time lag.

Einstein's New Idea

Einstein proposed that light consists of particles called photons. Each photon has energy proportional to its frequency, given by \( E = h u \), where \( E \) is the energy, \( h \) is Planck's constant, and \( u \) is the frequency of the light.

Threshold Frequency

The threshold frequency is the minimum frequency of light required to emit electrons from a metal surface. According to Einstein's idea, for electrons to be emitted, the energy of a photon (determined by its frequency) must be at least equal to the work function of the metal. Therefore, if the frequency is below a certain threshold, photons don't have enough energy to dislodge electrons from the metal's surface.

Absence of Time Lag

In the photoelectric effect, electrons are emitted almost instantaneously when light above the threshold frequency shines on the metal. This lack of delay can be explained by photon theory: electrons absorb the energy of individual photons in an all-or-nothing process. If a photon has sufficient energy, it will immediately transfer energy to an electron, causing its ejection without any time lag.

Key concepts

Einstein's Photon Theory

Einstein revolutionized our understanding of light by proposing that it doesn't just behave as a wave, but also as a particle. These particles are called photons.
Each photon carries a specific amount of energy, which depends on its frequency. You can calculate this energy using the formula:
\[ E = h u \] where: \( E \) is the energy, \( h \) is Planck's constant, and \( u \) is the frequency of the light.
This means that light with a higher frequency (like ultraviolet light) will have higher-energy photons than light with a lower frequency (like visible light).

• Photons interact with electrons in a metal surface to cause the emission
• If a photon's energy is too low, it won't dislodge an electron

Understanding photons helps explain phenomena like the photoelectric effect, where light causes electrons to be ejected from a metal surface.

Threshold Frequency

The threshold frequency is crucial in the photoelectric effect. It's the minimum frequency of light needed to eject electrons from a metal surface.
Why is this important? Einstein's photon theory tells us that the energy of a photon is directly proportional to its frequency:
\[ E = h u \] For an electron to be emitted, the energy from a single photon must be at least equal to the work function of the metal. The work function is the minimum energy needed to dislodge an electron.

Here's what happens if the photon's frequency is below the threshold:

• The photon's energy is too low to free an electron
• No electrons are emitted, no matter how intense the light is

If the frequency is above the threshold, electrons are emitted almost instantly. This explains why only certain frequencies of light can trigger the photoelectric effect.

Planck's Constant

Planck's constant is a fundamental quantity in quantum mechanics. It's represented by the symbol \(h\) and has a value of approximately \[ 6.626 \times 10^{-34} \] joule-seconds.
It acts as a bridge between the energy of a photon and its frequency, as shown in the formula:
\[ E = h u \] Planck's constant tells us how much energy one photon carries based on its frequency. Here's why it's important in the photoelectric effect:

• It helps calculate if a photon has enough energy to eject an electron
• It ties the energy of light directly to its frequency, explaining the threshold frequency