A photon of X-ray has energy of 1 keV. A photon of visible radiation has energy of 3 eV. In this context, which one of the following statements is not correct?
The speeds of both the photons in vacuum are different
Comparing X-ray and Visible Radiation Photons
This question asks us to compare the properties of two types of photons: an X-ray photon and a visible radiation photon. We are given their energies and asked to identify which statement about them is incorrect. To do this, we need to understand the relationship between energy, frequency, wavelength, and speed for photons.
Energy Comparison
The energy of the X-ray photon is given as 1 keV, and the energy of the visible radiation photon is 3 eV. Let's convert the X-ray energy to electron volts (eV) for easy comparison:
\[1 \text{ keV} = 1 \times 10^3 \text{ eV} = 1000 \text{ eV}\]
Comparing the energies:
- X-ray photon energy: 1000 eV
- Visible radiation photon energy: 3 eV
Clearly, the energies are different. The X-ray photon has significantly higher energy than the visible radiation photon.
Relationship Between Energy, Frequency, and Wavelength
The energy (\(E\)) of a photon is related to its frequency (\(\nu\)) by the equation:
\[E = h\nu\]
where \(h\) is Planck's constant.
The speed of light (\(c\)), frequency (\(\nu\)), and wavelength (\(\lambda\)) are related by:
\[c = \nu\lambda\]
From these equations, we can see:
- Energy is directly proportional to frequency (\(E \propto \nu\)). A higher energy photon has a higher frequency.
- Frequency is inversely proportional to wavelength (\(\nu \propto 1/\lambda\)). A higher frequency photon has a shorter wavelength.
- Therefore, energy is inversely proportional to wavelength (\(E \propto 1/\lambda\)). A higher energy photon has a shorter wavelength.
Analyzing the Statements
Let's evaluate each statement based on the energies and the relationships discussed:
Statement 1: The wavelength of X-ray photon is less than the wavelength of visible radiation photon.
The X-ray photon has higher energy (1000 eV) than the visible radiation photon (3 eV). Since energy is inversely proportional to wavelength, a higher energy means a shorter wavelength. Therefore, the wavelength of the X-ray photon should be less than the wavelength of the visible radiation photon. This statement is correct.
Statement 2: Both the photons have different energies.
As calculated earlier, the energy of the X-ray photon is 1000 eV, and the energy of the visible radiation photon is 3 eV. These energies are indeed different. This statement is correct.
Statement 3: The speeds of both the photons in vacuum are different.
Photons are quanta of electromagnetic radiation. All electromagnetic waves, regardless of their energy, frequency, or wavelength, travel at the same speed in a vacuum. This speed is the speed of light, denoted by \(c\), which is approximately \(3 \times 10^8\) meters per second. Therefore, the speed of an X-ray photon in vacuum is the same as the speed of a visible radiation photon in vacuum. This statement claims their speeds are different, which is incorrect.
Statement 4: The frequency of X-ray photon is higher than the frequency of visible radiation photon.
The X-ray photon has higher energy (1000 eV) than the visible radiation photon (3 eV). Since energy is directly proportional to frequency, a higher energy means a higher frequency. Therefore, the frequency of the X-ray photon should be higher than the frequency of the visible radiation photon. This statement is correct.
Conclusion
Based on our analysis, the statement that is not correct is that the speeds of both the photons in vacuum are different. All photons travel at the speed of light (\(c\)) in vacuum, irrespective of their type or energy.
| Property | X-ray Photon | Visible Radiation Photon | Comparison (X-ray vs Visible) |
|---|---|---|---|
| Energy (eV) | 1000 eV | 3 eV | Higher Energy |
| Frequency (\(\nu\)) | Higher | Lower | Higher Frequency (\(E \propto \nu\)) |
| Wavelength (\(\lambda\)) | Shorter | Longer | Shorter Wavelength (\(E \propto 1/\lambda\)) |
| Speed in Vacuum | \(c\) | \(c\) | Same Speed |
Revision Table: Photon Properties
Let's summarise the key properties of photons and their relationships:
- Photons are particles of light or electromagnetic radiation.
- The energy of a photon is proportional to its frequency: \(E = h\nu\).
- The speed of light, frequency, and wavelength are related: \(c = \nu\lambda\).
- In a vacuum, all photons travel at the same speed, \(c \approx 3 \times 10^8 \text{ m/s}\), regardless of their energy or type (radio waves, visible light, X-rays, etc.).
- Higher energy photons have higher frequency and shorter wavelength.
- Lower energy photons have lower frequency and longer wavelength.
Additional Information: Electromagnetic Spectrum
X-rays and visible light are both parts of the electromagnetic spectrum. The electromagnetic spectrum is the range of all types of electromagnetic radiation, ordered by frequency or wavelength. From lowest energy/frequency (longest wavelength) to highest energy/frequency (shortest wavelength), the spectrum includes:
- Radio waves
- Microwaves
- Infrared radiation
- Visible light
- Ultraviolet radiation
- X-rays
- Gamma rays
All of these types of radiation consist of photons, and all photons travel at the speed of light (\(c\)) in a vacuum. The difference between these types of radiation lies in their energy, frequency, and wavelength, which determines their interactions with matter.
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