Question

Which is more damaging to human tissue, a 60 -W source of visible light or a \(2 \cdot \mathrm{m} \mathrm{W}\) source of \(\mathrm{X}\) -rays? Explain your choice.

Short answer

Answer: The 2 mW source of X-rays has a higher potential to be damaging to human tissue than the 60 W source of visible light, due to the higher energy carried by X-ray photons, which can cause ionization and cell damage when interacting with human tissue.

Step-by-step solution

Understanding the units of measurement

Let's first make sure we understand the units given for the power of each source. A 60-W source of visible light means it emits 60 watts of power in the form of visible light. A 2 mW source of X-rays means it emits 2 milliwatts (0.002 watts) of power in the form of X-rays.

Comparing the power of the two sources

We can compare the power of the two sources directly since they are in the same unit of measurement (watts). With 60 watts of visible light and 2 milliwatts of X-rays, we can see that the source of visible light emits much more power than the source of X-rays, by a factor of 30,000 (60 / 0.002).

Understanding the energy carried by the waves

Now let's discuss the energy carried by these waves. Visible light waves have lower energy than X-ray waves. This is because the energy of a photon is proportional to its frequency and inversely proportional to its wavelength, as given by the equation E=hf (where E is the energy, h is the Planck's constant, and f is the frequency). X-rays have higher frequencies (and smaller wavelengths) than visible light, which means their photons carry more energy.

Considering the interaction with human tissue

The energy carried by the photons is critical when considering the damage done to human tissue. Higher energy photons have a greater potential to ionize atoms, which can lead to cell damage and DNA mutations. Since X-ray photons have higher energy than visible light photons, they can be more damaging to human tissue even though the power of the X-ray source is much lower than the visible light source.

Final answer

Considering the interaction of the photons with human tissue, we can conclude that the 2 mW source of X-rays has a higher potential to be damaging to human tissue than the 60 W source of visible light, despite having much lower power emission. This is due to the higher energy carried by X-ray photons, which can cause ionization and cell damage when interacting with human tissue.

Key concepts

Ionizing Radiation

Ionizing radiation is a type of energy released by atoms in the form of electromagnetic waves or particles. It is powerful enough to remove tightly bound electrons from the orbit of an atom, causing the atom to become charged or ionized.

Examples of ionizing radiation include X-rays, gamma rays, and alpha and beta particles. The unique characteristic of ionizing radiation is its ability to cause damage to living tissue at the atomic and molecular level. This property comes from the high energy carried by the particles or electromagnetic waves that compose ionizing radiation.

The biological effects of ionizing radiation may include cell damage, DNA mutations, and cancer, making it a significant concern in medical treatments, nuclear power generation, and other fields where radiation is present.

Photon Energy

The concept of photon energy is vital for understanding how light interacts with matter. A photon is a discrete packet of electromagnetic energy, and its energy can be calculated using the equation \( E = hf \), where \( E \) is the energy, \( h \) is Planck's constant (approximately \( 6.626 \times 10^{-34} \) Joule seconds), and \( f \) is the frequency of the electromagnetic wave.

Photons with higher frequencies have more energy, which enables them to affect matter more significantly. For example, X-rays have high-frequency photons that can penetrate deeply into human tissue and even ionize atoms and molecules, leading to biological changes.

Interaction of Photons with Human Tissue

When photons interact with human tissue, their energy plays a crucial role in determining the outcome. Low-energy photons, such as those from visible light, typically pass through or are absorbed by the tissue without causing significant changes at the atomic level.

On the other hand, high-energy photons, like those from X-ray sources, have enough energy to displace electrons from atoms or molecules within the tissue, leading to ionization. This can result in disruption of cellular function, DNA damage, and possibly even cancer if cell repair mechanisms fail.

The ability of different photons to cause damage depends on both their energy and their absorption by tissue, which is related to factors such as photon energy, tissue type, and exposure duration.

Power Emission of Light Sources

The power emission of a light source, measured in watts, denotes the rate at which energy is emitted in the form of light. This helps us quantify the amount of light produced over time. However, it's not solely the amount of power that determines the potential damage to human tissue.

When considering two light sources of vastly different energies, such as visible light and X-rays, the power emitted doesn’t directly correlate with potential harm. A lower power emission of a high-energy light source like X-rays can be far more damaging than a higher power emission of a low-energy light source, like visible light. This is due to the ionization potential of X-rays, which can lead to more profound biological effects than the primarily heating effect of visible light.