Question

The wavelength of \(\mathrm{x}\) rays is of the order of (A) \(1 \mathrm{~cm}\) (B) \(1 \mathrm{~m}\) (C) Imicron (D) 1angstrom

Short answer

The wavelength of x-rays is of the order of 1 angstrom, which falls within the x-ray wavelength range of \(10^{-9}\) m to \(10^{-12}\) m. Therefore, the correct answer is (D).

Step-by-step solution

1. Compare with standard x-ray wavelength range

First, we need to know the standard wavelength range of x-rays. The wavelength of x-rays typically falls within the range of \(10^{-9}\) m (nanometer) to \(10^{-12}\) m (picometer). We will compare each given option with this range to find the correct answer.

2. Convert units and compare

We will now convert each given option to meters so that we can compare them with the standard x-ray wavelength range. (A) \(1 \: cm = 1 \times 10^{-2} \: m\) (B) \(1 \: m\) (C) 1 micron (micrometer) = \(1 \times 10^{-6} \: m\) (D) 1 angstrom = \(1 \times 10^{-10} \: m\)

3. Choose the correct option

Now, let's compare each of these converted options with the standard x-ray wavelength range: (A) \(1 \times 10^{-2} \: m\) is far too large for an x-ray wavelength. (B) \(1 \: m\) is also too large for an x-ray wavelength. (C) \(1 \times 10^{-6} \: m\) is smaller than the range of x-ray wavelengths, but it is still larger than the usual x-ray wavelengths. (D) \(1 \times 10^{-10} \: m\) falls within the x-ray wavelength range, indicating that this is the correct answer. So, the wavelength of x-rays is of the order of 1 angstrom. The correct answer is (D).