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Which of the following statements are tr...

Which of the following statements are true?

A

The shortest wavelength of X-rays emitted from an X-ray tube depends on the corrent in the tube.

B

Characteristic X-ray spectra is simple as compared to optical spectra.

C

X-ray cannot be different by means of an ordianary grating.

D

Three exist a sharp limit on the short wavelength side for each continous X-ray spectrum

Text Solution

AI Generated Solution

The correct Answer is:
To determine which statements about X-rays are true, we will analyze each option one by one. ### Step-by-Step Solution: 1. **Analyze Option A**: - Statement: "The shortest wavelength of X-ray emitted from the X-ray tube depends upon the current in the tube." - Explanation: The energy of X-rays emitted from an X-ray tube is given by the equation \( E = \frac{hc}{\lambda} \), where \( E \) is the energy, \( h \) is Planck's constant, \( c \) is the speed of light, and \( \lambda \) is the wavelength. The energy \( E \) is primarily determined by the voltage applied to the tube, not the current. Therefore, this statement is **false**. 2. **Analyze Option B**: - Statement: "Characteristic X-ray spectra is simple compared to the optical spectra." - Explanation: Characteristic X-ray spectra consist of sharp peaks at specific wavelengths corresponding to the transitions of electrons between energy levels in atoms. In contrast, optical spectra can be more complex and continuous. Thus, this statement is **true**. 3. **Analyze Option C**: - Statement: "X-ray cannot be diffracted by the means of the ordinary grating." - Explanation: X-rays have very short wavelengths and can penetrate ordinary gratings. To diffract X-rays, a grating with a spacing comparable to the wavelength of X-rays is required, which is not the case with ordinary gratings. Therefore, this statement is **true**. 4. **Analyze Option D**: - Statement: "There exist sharp limits on the short wavelength side for each continuous X-ray spectrum." - Explanation: In a continuous X-ray spectrum, there is a cut-off wavelength determined by the maximum energy of the electrons striking the target, which corresponds to the maximum voltage applied. This means there is indeed a sharp limit on the short wavelength side. Thus, this statement is **true**. ### Conclusion: - The correct options are **B, C, and D**.

To determine which statements about X-rays are true, we will analyze each option one by one. ### Step-by-Step Solution: 1. **Analyze Option A**: - Statement: "The shortest wavelength of X-ray emitted from the X-ray tube depends upon the current in the tube." - Explanation: The energy of X-rays emitted from an X-ray tube is given by the equation \( E = \frac{hc}{\lambda} \), where \( E \) is the energy, \( h \) is Planck's constant, \( c \) is the speed of light, and \( \lambda \) is the wavelength. The energy \( E \) is primarily determined by the voltage applied to the tube, not the current. Therefore, this statement is **false**. ...
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