Photon Energy Calculation A Step-by-Step Physics Guide

Hey everyone! Ever wondered how much energy a single photon carries? It might seem like a tiny amount, but when you're dealing with light and other electromagnetic radiation, these little packets of energy really add up. Today, we're going to dive into a fun physics problem where we calculate the energy of a photon given its frequency. We'll use Planck's famous equation, which is the key to unlocking this mystery. So, grab your calculators and let's get started!

Understanding the Problem

Before we jump into the calculations, let's make sure we understand the problem. We're given a photon with a frequency of 7.3 x 10^-17 Hz. Frequency, in simple terms, tells us how many wave cycles pass a point in one second. The unit Hertz (Hz) means "cycles per second." We also know Planck's constant, which is a fundamental constant in quantum mechanics, and it's given as 6.63 x 10^-34 J·s. Our mission is to find the energy of this photon, and we need to express our answer to the nearest tenths place, in the form of something times 10^-50 J. That might seem like a super small number, and you're right, it is! But that's the scale we're working with when we talk about individual photons.

The core concept here is the relationship between a photon's energy and its frequency. This relationship is beautifully captured by Planck's equation, which is the cornerstone of quantum mechanics. It tells us that energy is not continuous but comes in discrete packets, or quanta, which we call photons in the case of light. This was a revolutionary idea that changed our understanding of the universe at a fundamental level. Imagine thinking of light not just as a wave, but also as a stream of tiny particles, each carrying a specific amount of energy! This dual nature of light – wave and particle – is one of the most fascinating aspects of quantum physics. So, with this understanding in place, let's move on to the equation that will help us solve the problem.

Planck's Equation: The Key to Photon Energy

The equation we need is called Planck's equation, and it's a simple yet powerful formula: E = hν, where:

• E is the energy of the photon (what we want to find)
• h is Planck's constant (6.63 x 10^-34 J·s)
• ν (the Greek letter nu) is the frequency of the photon (7.3 x 10^-17 Hz)

This equation tells us that the energy of a photon is directly proportional to its frequency. This means that a photon with a higher frequency will have more energy, and a photon with a lower frequency will have less energy. It's a linear relationship, which makes it easy to understand and use. The constant of proportionality is Planck's constant, which is a tiny number, reflecting the small scale of energy involved at the quantum level.

Planck's equation is not just a formula; it's a cornerstone of quantum mechanics. It was introduced by Max Planck in 1900, and it marked a turning point in physics. Before Planck, it was thought that energy could be emitted or absorbed in any amount. But Planck's work showed that energy is actually quantized, meaning it comes in discrete packets. This idea was so revolutionary that it eventually led to the development of quantum mechanics, which is the theory that describes the behavior of matter and energy at the atomic and subatomic levels. So, when we use Planck's equation, we're not just doing a simple calculation; we're tapping into one of the most profound discoveries in the history of physics. Now that we understand the equation, let's plug in the numbers and find the energy of our photon.

Plugging in the Values and Calculating

Now comes the fun part – putting the numbers into the equation and crunching them! We have:

• h = 6.63 x 10^-34 J·s
• ν = 7.3 x 10^-17 Hz

So, E = (6.63 x 10^-34 J·s) x (7.3 x 10^-17 Hz). Grab your calculators, guys, and let's do this! When you multiply these two numbers together, you get approximately 4.84 x 10^-50 J. But wait, we're not quite done yet. The problem asks us to express the answer to the nearest tenths place, in the form of something times 10^-50 J. We already have the 10^-50 J part, so we just need to round 4.84 to the nearest tenth. This gives us 4.8. So, the energy of the photon is approximately 4.8 x 10^-50 J.

It's important to pay attention to the units in these calculations. Planck's constant has units of J·s (joule-seconds), and the frequency has units of Hz (Hertz), which is equivalent to s^-1 (per second). When we multiply these together, the seconds cancel out, leaving us with joules (J), which is the unit of energy. This is a good way to check that we've set up the problem correctly. If the units didn't work out, we'd know we'd made a mistake somewhere. Another thing to keep in mind is significant figures. In this case, both Planck's constant and the frequency are given to two significant figures, so our answer should also be rounded to two significant figures. We've done that by rounding 4.84 to 4.8. So, we've successfully calculated the energy of the photon using Planck's equation!

Expressing the Answer in the Required Format

Alright, we've done the hard work of calculating the energy, but we need to present our answer in the specific format the problem asks for: something x 10^-50 J, to the nearest tenths place. We've already got the 10^-50 J part, and we've rounded our result to the nearest tenth, which gave us 4.8. So, the final step is simply to write our answer in the blank space provided. It's like putting the last piece of a puzzle in place! Sometimes, especially in physics problems, the way you present your answer is just as important as the calculation itself. It shows that you understand the question fully and can communicate your results clearly.

Think of it like this: you've built a beautiful house (solved the problem), but you need to put a nice coat of paint on it (format the answer) so everyone can appreciate your work. In this case, the "coat of paint" is expressing our answer in the specific format requested. This is a common practice in scientific and engineering fields, where clarity and precision are paramount. It ensures that your results can be easily understood and used by others. So, make sure you always double-check the instructions and present your answers in the required format. With that final step completed, we can confidently say that we've solved the problem and expressed our answer in the correct way.

Final Answer and Implications

So, there you have it! The energy of the photon, to the nearest tenths place, is 4.8 x 10^-50 J. That's a tiny amount of energy, but it's the energy carried by a single photon with a frequency of 7.3 x 10^-17 Hz. This might seem like just a number, but it has some pretty cool implications when you think about it. This calculation demonstrates the quantized nature of light. Remember, Planck's equation tells us that energy comes in discrete packets, or photons. The energy of each photon is directly proportional to its frequency. So, photons with higher frequencies (like ultraviolet or X-rays) carry much more energy than photons with lower frequencies (like infrared or radio waves).

This concept is fundamental to many areas of physics and technology. For example, it explains why ultraviolet light can cause sunburn, while visible light doesn't. The higher-energy photons in ultraviolet light can damage our skin cells. It's also the basis for technologies like lasers and solar cells. Lasers use the principle of stimulated emission to produce beams of light with a specific frequency and energy. Solar cells use the energy of photons from sunlight to generate electricity. So, understanding the energy of photons is not just an academic exercise; it has real-world applications that impact our daily lives. By calculating the energy of this photon, we've taken a small step into the fascinating world of quantum mechanics and its many applications. Keep exploring, guys, there's so much more to discover!