📚 Photon Energy Formula and Typical Calculations | 光子能量公式与典型计算
In A-Level physics, the photon model describes light as a stream of discrete particles, each carrying a quantum of energy. The energy of a single photon is given by the Planck-Einstein relation, which links the frequency of electromagnetic radiation to the energy it carries. Understanding this formula is essential for topics such as the photoelectric effect, atomic spectra, and wave-particle duality.
在 A-Level 物理中，光子模型将光描述为一连串离散的粒子，每个粒子携带一份能量量子。单个光子的能量由普朗克-爱因斯坦关系式给出，它将电磁辐射的频率与其所携带的能量联系起来。理解这个公式对于光电效应、原子光谱和波粒二象性等主题至关重要。
1. The Concept of Quantised Energy | 能量量子化的概念
Max Planck proposed that electromagnetic energy is emitted or absorbed in discrete packets, called quanta. Each quantum has energy proportional to its frequency. This idea departed from classical wave theory, which allowed any continuous amount of energy.
马克斯·普朗克提出，电磁能量以称为量子的离散包形式发射或吸收。每个量子的能量与其频率成正比。这一观念背离了经典波动理论，后者允许任何连续的能量数值。
The photon is the particle-like quantum of light. Albert Einstein extended Planck’s idea by treating light itself as a stream of photons, each with energy E = hf. This directly explained the photoelectric effect.
光子是光的粒子性量子。阿尔伯特·爱因斯坦将普朗克的思想加以延伸，将光本身视为一串光子，每个光子具有能量 E = hf。这直接解释了光电效应。
2. The Photon Energy Formula: E = hf | 光子能量公式：E = hf
The fundamental formula for photon energy is:
光子能量的基本公式为：
E = hf
Here, E is the energy in joules (J), f is the frequency of the electromagnetic wave in hertz (Hz), and h is the Planck constant, approximately 6.63 × 10⁻³⁴ J s.
其中，E 是以焦耳 (J) 为单位的能量，f 是电磁波的频率，单位为赫兹 (Hz)，h 是普朗克常数，约为 6.63 × 10⁻³⁴ J s。
Because frequency is related to wavelength by c = fλ, the formula can be written in terms of wavelength:
由于频率与波长的关系为 c = fλ，因此公式也可以用波长来表达：
E = hc / λ
where c is the speed of light in a vacuum (3.00 × 10⁸ m s⁻¹) and λ is the wavelength in metres.
其中 c 是真空中的光速 (3.00 × 10⁸ m s⁻¹)，λ 是以米为单位的波长。
The table below summarises the key relationships used in photon calculations.
下表总结了光子计算中使用的关键关系式。
| Relationship | When to use it |
| E = hf | Given frequency |
| E = hc / λ | Given wavelength |
| p = h / λ | Photon momentum |
3. Units and Constants | 单位与常数
In CIE A-Level physics, you must use SI units in calculations. Planck’s constant is usually given as h = 6.63 × 10⁻³⁴ J s. The speed of light is c = 3.00 × 10⁸ m s⁻¹. Frequency is in Hz, which is equivalent to s⁻¹.
在 CIE A-Level 物理中，计算时必须使用国际单位制。普朗克常数通常给出为 h = 6.63 × 10⁻³⁴ J s。光速为 c = 3.00 × 10⁸ m s⁻¹。频率的单位是 Hz，相当于 s⁻¹。
- Wavelength must be in metres; convert nm to m by dividing by 10⁹.
- 波长必须换算为米；将纳米除以 10⁹ 转换为米。
- Energy is in joules, but electronvolts (eV) are often used in atomic physics.
- 能量以焦耳为单位，但在原子物理中常用电子伏特 (eV)。
- Always check whether the final answer is a reasonable magnitude for the type of radiation.
- 始终检查最终答案的数量级是否与该辐射类型相符。
4. Calculating Photon Energy from Frequency | 由频率计算光子能量
Example: A radio wave has a frequency of 98.0 MHz. Calculate the energy of a single photon.
示例：一个无线电波的频率为 98.0 MHz。计算单个光子的能量。
First convert MHz to Hz: 98.0 MHz = 98.0 × 10⁶ Hz. Then apply E = hf:
先将 MHz 转换为 Hz：98.0 MHz = 98.0 × 10⁶ Hz。然后应用 E = hf：
E = (6.63 × 10⁻³⁴ J s) × (98.0 × 10⁶ s⁻¹) = 6.50 × 10⁻²⁶ J
The answer is roughly 6.50 × 10⁻²⁶ J. Note that radio photons have extremely small energies.
答案约为 6.50 × 10⁻²⁶ J。注意无线电光子的能量非常小。
Another example: X-rays with frequency 3.00 × 10¹⁸ Hz have photon energy:
另一个例子：频率为 3.00 × 10¹⁸ Hz 的 X 射线，其光子能量为：
E = (6.63 × 10⁻³⁴) × (3.00 × 10¹⁸) ≈ 1.99 × 10⁻¹⁵ J
Higher frequency means higher photon energy, so X-rays carry much more energy than radio waves.
频率越高，光子能量越大，因此 X 射线比无线电波携带的能量大得多。
5. Calculating Photon Energy from Wavelength | 由波长计算光子能量
Example: Green light has a wavelength of 550 nm. Find the photon energy in joules.
示例：绿光的波长为 550 nm。求光子能量（以焦耳为单位）。
Convert wavelength to metres: λ = 550 × 10⁻⁹ m. Use E = hc / λ:
将波长换算为米：λ = 550 × 10⁻⁹ m。使用 E = hc / λ：
E = (6.63 × 10⁻³⁴) × (3.00 × 10⁸) / (550 × 10⁻⁹) ≈ 3.62 × 10⁻¹⁹ J
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