Hey guys! Ever wondered about the frequency of light? Specifically, what happens when we're talking about photons and their wavelengths? This is a super cool topic in physics, and we're going to dive deep into how to calculate the frequency of a photon given its wavelength. So, let's get started and unlock the secrets of light!
In the realm of physics, understanding the relationship between wavelength and frequency is fundamental. These two properties are inversely proportional, meaning that as one increases, the other decreases. This relationship is elegantly described by a simple yet powerful equation:
Where:
crepresents the speed of light in a vacuum, a universal constant approximately equal to $3.0 imes 10^8 m/s$.-
\lambda$ (lambda) denotes the wavelength, which is the distance between successive crests or troughs of a wave. It's usually measured in meters (m).
-
\nu$ (nu) symbolizes the **frequency**, which is the number of waves that pass a given point per unit of time. It's measured in Hertz (Hz), where 1 Hz is equal to 1 wave per second.
This equation is a cornerstone in understanding electromagnetic radiation, which encompasses everything from radio waves to gamma rays. Each type of electromagnetic radiation has its unique wavelength and frequency, but they all travel at the same speed – the speed of light. This constant speed links these two properties together, allowing us to calculate one if we know the other. For example, if we know the wavelength of a photon, we can easily determine its frequency using the formula above. This principle is crucial in various applications, including telecommunications, medical imaging, and even understanding the colors we see.
Now, let's put this knowledge into action and calculate the frequency of a photon with a given wavelength. We have a photon with a wavelength of $4.5 imes 10^{-4} m$. To find its frequency, we'll use the formula we discussed earlier:
We need to rearrange this formula to solve for frequency ($\nu$):
We know the speed of light, $c = 3.0 imes 10^8 m/s$, and the wavelength, $\lambda = 4.5 imes 10^{-4} m$. Now we just plug in the values:
Let's do the math:
To express this in scientific notation, we adjust the decimal point:
So, the frequency of a photon with a wavelength of $4.5 imes 10^{-4} m$ is approximately $6.67 imes 10^{11} Hz$.
Okay, guys, now that we've calculated the frequency, let's take a look at the options given and see which one matches our result. We have the following choices:
A. $2.98 imes 10^{-37} Hz$ B. $1.47 imes 10^{-30} Hz$ C. $1.35 imes 10^5 Hz$ D. $6.67 imes 10^{11} Hz$
Our calculated frequency was $6.67 imes 10^{11} Hz$. Looking at the options, it's clear that option D, $6.67 imes 10^{11} Hz$, perfectly matches our result. This means that the correct answer is D. The other options are significantly different from our calculated value, so we can confidently rule them out. Option A and B have extremely low frequencies, which are not realistic for photons with the given wavelength. Option C has a frequency that is several orders of magnitude smaller than our result.
Understanding the relationship between wavelength and frequency isn't just about plugging numbers into a formula; it's about grasping the fundamental nature of light and electromagnetic radiation. This concept is crucial in various fields, from telecommunications to medicine. For example, in telecommunications, different frequencies of radio waves are used to transmit information. In medicine, X-rays (which have very high frequencies and short wavelengths) are used for imaging bones, while MRI (which uses radio waves with much lower frequencies) is used for soft tissue imaging.
The frequency of light also determines its energy. Higher frequency photons carry more energy. This is why ultraviolet light (which has a higher frequency than visible light) can cause sunburn, and gamma rays (which have extremely high frequencies) are used in cancer treatment. Understanding these relationships helps us harness the power of electromagnetic radiation for various applications while also being mindful of its potential risks. So, the next time you see a rainbow or use your cell phone, remember the fundamental physics that makes it all possible!
When calculating the frequency of a photon, there are a few common mistakes that students often make. One of the most frequent errors is incorrectly rearranging the formula $c = \lambda \nu$. Remember, to solve for frequency ($\nu$), you need to divide the speed of light (c) by the wavelength ($\lambda$). Make sure you don't accidentally multiply them or divide in the wrong order!
Another common mistake is using the wrong units. Wavelength should be in meters (m), and the speed of light is in meters per second (m/s). If your wavelength is given in a different unit, like nanometers (nm) or micrometers (µm), you'll need to convert it to meters before plugging it into the formula. Similarly, make sure your final answer is in Hertz (Hz), which is the standard unit for frequency.
Finally, pay close attention to scientific notation. When dealing with very large or very small numbers, it's easy to make mistakes with the exponents. Double-check your calculations, and if you're using a calculator, be sure you know how to enter numbers in scientific notation correctly. Avoiding these common pitfalls will help you accurately calculate photon frequencies and ace your physics problems!
So, there you have it, guys! We've successfully calculated the frequency of a photon given its wavelength and seen how this calculation fits into the broader context of physics. Remember, the key is understanding the relationship $c = \lambda \nu$ and applying it carefully. Keep practicing, and you'll be a pro at photon frequency calculations in no time! Physics is all about understanding the world around us, and every calculation we do brings us one step closer to that understanding. Keep exploring, keep questioning, and most importantly, keep learning!