Estimating the following two numbers should be interesting. The first number will tell you why radio engineers do not need to worry much about photons! The second number tells you why our eye can never ‘count photons’, even in barely detectable light. (a) The number of photons emitted per second by a Medium wave transmitter of 10 kW power, emitting radiowaves of wavelength 500 m.

To estimate the number of photons emitted per second by a medium wave transmitter with a power of 10 kW and a wavelength of 500 m, we can use a straightforward approach based on the relationship between energy, power, and the properties of photons. Let’s break this down step by step.

Understanding Photon Emission

First, we need to recognize that photons are quantized packets of energy. The energy of a single photon can be calculated using the formula:

E = h * f

Where:

• E is the energy of the photon.
• h is Planck's constant (approximately 6.626 x 10^-34 J·s).
• f is the frequency of the electromagnetic wave.

Calculating Frequency

Next, we need to find the frequency of the radio wave. The frequency can be derived from the speed of light (c) and the wavelength (λ) using the formula:

f = c / λ

Here, the speed of light (c) is approximately 3 x 10⁸ m/s, and the wavelength (λ) is given as 500 m. Plugging in these values:

f = (3 x 10⁸ m/s) / (500 m) = 6 x 10⁵ Hz

Calculating Energy per Photon

Now that we have the frequency, we can calculate the energy of a single photon:

E = (6.626 x 10^-34 J·s) * (6 x 10⁵ Hz) ≈ 3.976 x 10^-28 J

Finding the Number of Photons Emitted

With the energy of a single photon known, we can now determine how many photons are emitted per second by the transmitter. The power (P) of the transmitter is given as 10 kW, which is equivalent to 10,000 W. Power is defined as energy per unit time, so we can express this as:

P = E_total / t

Rearranging this gives us:

E_total = P * t

For one second, this simplifies to:

E_total = 10,000 J

Calculating the Number of Photons

To find the total number of photons emitted per second (N), we divide the total energy emitted in one second by the energy of a single photon:

N = E_total / E

Substituting the values we have:

N = 10,000 J / (3.976 x 10^-28 J) ≈ 2.51 x 10³¹ photons

Implications of the Result

This enormous number of photons—approximately 2.51 x 10³¹—illustrates why radio engineers don’t need to worry much about individual photons. The sheer volume of photons emitted means that even in less-than-ideal conditions, there will be plenty of photons available for detection and communication.

In contrast, the second part of your question relates to why our eyes cannot 'count' photons, particularly in low-light conditions. The human eye is sensitive to light but operates on a different scale. Even in dim light, the number of photons hitting the retina is often far below the threshold needed for reliable detection, making it impossible to count them accurately. This is due to the biological limitations of photoreceptor cells in our eyes, which can only respond to a certain range of light intensities.

In summary, while radio engineers deal with an overwhelming number of photons, our eyes are limited in their ability to detect and quantify them, especially in low-light scenarios. This distinction highlights the fascinating interplay between physics and biology in our perception of the world.

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