Photons of an electromagnetic radiation has an energy 11 keV each. To which region of electromagnetic spectrum does it belong?

The energy of each photon is given as 11 keV. To determine the region of the electromagnetic spectrum, we need to find the wavelength of the radiation. The energy $$E$$ of a photon is related to its wavelength $$\lambda$$ by the formula:

$$E = \frac{hc}{\lambda}$$

where $$h$$ is Planck's constant and $$c$$ is the speed of light. Rearranging for $$\lambda$$, we get:

$$\lambda = \frac{hc}{E}$$

First, convert the energy from keV to eV. Since 1 keV = 1000 eV,

$$E = 11 \text{ keV} = 11 \times 1000 = 11000 \text{ eV}$$

To simplify the calculation, we use the formula that directly relates wavelength in angstroms (Å) to energy in eV:

$$\lambda (\text{Å}) = \frac{12400}{E (\text{eV})}$$

This formula comes from the constant $$hc \approx 12400 \text{ eV} \cdot \text{Å}$$. Substituting $$E = 11000 \text{ eV}$$:

$$\lambda = \frac{12400}{11000}$$

Simplify the fraction by dividing numerator and denominator by 100:

$$\lambda = \frac{124}{110}$$

Further simplify by dividing both by 2:

$$\lambda = \frac{62}{55}$$

Now, perform the division:

$$\lambda = \frac{62}{55} \approx 1.12727 \text{Å}$$

So, the wavelength is approximately 1.127 Å.

Now, recall the approximate wavelength ranges for different regions of the electromagnetic spectrum:

• X-ray region: 0.1 Å to 100 Å
• Ultraviolet (UV) region: 100 Å to 4000 Å
• Visible region: 4000 Å to 7000 Å
• Infrared (IR) region: above 7000 Å

The calculated wavelength of 1.127 Å falls within the range of 0.1 Å to 100 Å, which corresponds to the X-ray region.

Hence, the correct answer is Option A.