understand and use the terms threshold frequency and threshold wavelength

Energy and Momentum of a Photon

What is a Photon?

A photon is the smallest packet of light energy. Think of it as a tiny, invisible ball that can behave like a wave or a particle, depending on the experiment. 🌟

Energy of a Photon

Photons carry energy that depends on how fast they oscillate – their frequency. The relationship is:

$$E = hu$$

• $h$ is Planck’s constant (≈ $6.626\times10^{-34}$ J·s).
• $u$ is the frequency (Hz).
• Higher frequency → more energy.

Momentum of a Photon

Even though photons have no mass, they still carry momentum:

$$p = \frac{h}{\lambda}$$

• $\lambda$ is the wavelength (m).
• Shorter wavelength → larger momentum.

Threshold Frequency

In the photoelectric effect, electrons are ejected from a metal only if the incoming photons have a minimum frequency, called the threshold frequency ($u_0$). The condition is:

$$hu_0 = \phi$$

• $\phi$ is the work function of the metal (energy needed to free an electron).
• Photons with $u < u_0$ cannot eject electrons.

Threshold Wavelength

Because frequency and wavelength are inversely related ($c = u\lambda$), we can also talk about a threshold wavelength ($\lambda_0$). The relationship is:

$$\lambda_0 = \frac{c}{u_0}$$

• Longer wavelength (lower frequency) → photon energy too low.
• Shorter wavelength (higher frequency) → enough energy to eject electrons.

Key Formulae

Exam Tips

Analogy: Photon as a Tiny Light Ball

Imagine a photon as a tiny, glowing marble that can bounce off a surface. If the marble is heavy (high energy), it can knock other marbles (electrons) off the surface. If it’s light (low energy), it just glides by. The threshold frequency is like the minimum weight the marble needs to lift another marble.

Key Takeaways

• Energy: $E = hu$ – higher frequency, higher energy.
• Momentum: $p = h/\lambda$ – shorter wavelength, larger momentum.
• Threshold frequency ($u_0$) is the minimum frequency to free an electron.
• Threshold wavelength ($\lambda_0$) is the longest wavelength that still has enough energy.
• Always check units and remember $c = u\lambda$ when converting.