Show that a conventional x-ray generator is incapable of generating x-rays of wavelength as low as 10-11m. Do this by determining the identity of the target (in atomic number, Z) which would be needed to generate such x-rays.

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110 To determine whether a conventional x-ray generator is capable of generating x-rays with a wavelength as low as 10^(-11) m, we need to consider the limitations imposed by the technology.

X-rays are produced when high-energy electrons impact a target material. The energy of the x-rays generated is related to the energy of the electrons, according to the equation E = hc/λ, where E is the energy of the x-rays, h is the Planck's constant, c is the speed of light, and λ is the wavelength of the x-rays.

A conventional x-ray generator typically operates in the range of 10^4 - 10^6 volts (eV), depending on the system. To find out whether such a generator can produce x-rays with a wavelength of 10^(-11) m, we need to calculate the corresponding x-ray energy.

Using the energy-wavelength relationship, rearranged as λ = hc/E, we can calculate the energy:

E = hc/λ = (6.626 x 10^(-34) Js × 3 x 10^8 m/s)/(10^(-11) m) ≈ 2 x 10^(-17) J

Next, we convert the energy from joules to electron volts (eV) using the conversion factor: 1 J = 6.242 x 10^18 eV.

E(eV) = (2 x 10^(-17) J) × (6.242 x 10^18 eV/J) ≈ 1.248 x 10^2 eV

From this calculation, we can see that generating x-rays with a wavelength of λ = 10^(-11) m would require an x-ray energy of approximately 1.248 x 10^2 eV.

In terms of the target material, the x-ray energy depends on the atomic number (Z) of the material. X-ray production involves the interaction of high-energy electrons with the target material's atoms. Higher atomic numbers generally result in higher-energy x-rays.

To generate x-rays with the required energy of approximately 1.248 x 10^2 eV, a target material with a suitable atomic number is needed. Based on the periodic table, elements with moderately high atomic numbers, such as iodine (Z = 53) or antimony (Z = 51), could be suitable target materials for generating x-rays with the desired energy.

Therefore, a conventional x-ray generator, operating with voltages in the range of 10^4 - 10^6 volts, would require a target material with a relatively high atomic number (such as iodine or antimony) to generate x-rays with a wavelength as low as 10^(-11) m.