Question

Which of the following are true?
(This question has multiple correct options)
A. The shortest wavelength of X-rays emitted from an X-ray tube depends on the current in the tube.
B. Characteristic X-ray spectra are simple as compared to optical spectra.
C. X-rays cannot be diffracted by means of an ordinary grating.
D. There exists a sharp limit on the short wavelength side for each continuous X-ray spectrum.

Answer 1

Hint:If the electrons are accelerated through a potential difference V and then are incident on a suitable target, X-rays of wavelength equal or more than $${\displaystyle \frac{hc}{eV}}$$ are produced.

Therefore, they depend on the voltage applied.

The X-ray spectrum is classified into two types:
1. Continuous X-ray spectrum having all sorts of wavelengths and does not have a peak in the
spectra.
2. Characteristic X-ray spectrum having distinct wavelengths and do have a peak in the spectra.

Formula Used:The minimum wavelength of X-rays is given by: $$\lambda ={\displaystyle \frac{1240}{V}}nm$$.

Complete step by step solution:The shortest X-rays wavelength emitted when the electrons incident on the target are accelerated through potential V will be $$\lambda ={\displaystyle \frac{hc}{eV}}={\displaystyle \frac{1240}{V}}nm$$ .

Therefore, the shortest wavelength of X-rays emitted from an X-ray tube is inversely proportional to the voltage and not the current.

Hence, option (A) is not the correct answer.

In optical spectra, the number of frequencies of light an atom can emit depends upon the states of the electron. The characteristic X-rays for most of the elements consist of K and L series. Frequency of characteristic X-rays is directly proportional to $$Z^2$$ , where $$Z$$ is the atomic number and depends on atomic numbers. Thus, characteristic X-ray spectra are simple as compared to optical spectra.

X-rays have very short wavelengths that are shorter than the spacing between two lines in the grating.
Therefore, X-rays cannot be diffracted by means of ordinary grating.
When the incident electrons penetrate the atom of the target and go past the nucleus, they are retarded, due to which X-rays are emitted. The X-rays produced are called continuous X-rays. The minimum wavelength of X-rays is given by $$\lambda ={\displaystyle \frac{1240}{V}}nm$$.

Therefore, there exists a sharp limit on the short wavelength side for each continuous X-ray spectrum.

Hence, option (B), (C) and (D) are the correct answers.

Note:The characteristic X-ray spectra are simple as compared to optical spectra. But the X-ray spectra and the optical spectra differ widely in the range of wavelengths. (This is the exceptional case). The range of wavelengths for optical spectra is from $$300nm-700nm$$ and that for X-rays is from$$1nm-1pm$$.