Question:
The cut-off wavelength for the continuous X-rays coming from an X-ray tube operating at 30 kV is:
The cut-off wavelength for the continuous X-rays coming from an X-ray tube operating at 30 kV is:
Show Hint
Use the Duane-Hunt law: lambda_min = 12400 / V (in eV) angstrom, then convert. 12400/30000 = 0.414 angstrom = 41.4 pm.
Updated On: Jul 2, 2026
- 41.4 nm
- 41.4 Å
- 41.4 pm
- 41.4 µm
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: The cut-off (minimum) wavelength of continuous X-rays occurs when an electron accelerated through the tube voltage \(V\) converts all of its kinetic energy into a single photon:
\[ eV = \frac{hc}{\lambda_{\min}}. \]
Step 2: Solving for \(\lambda_{\min}\) and using the standard shortcut \(hc/e = 12400\ \text{eV}\cdot\text{\AA}\):
\[ \lambda_{\min} = \frac{hc}{eV} = \frac{12400\ \text{eV}\cdot\text{\AA}}{30000\ \text{eV}}. \]
Step 3: Evaluate:
\[ \lambda_{\min} = 0.4133\ \text{\AA} = 0.4133 \times 10^{-10}\ \text{m} = 41.3\ \text{pm}. \]
This matches 41.4 pm.
\[\boxed{\lambda_{\min} \approx 41.4\ \text{pm}}\]
\[ eV = \frac{hc}{\lambda_{\min}}. \]
Step 2: Solving for \(\lambda_{\min}\) and using the standard shortcut \(hc/e = 12400\ \text{eV}\cdot\text{\AA}\):
\[ \lambda_{\min} = \frac{hc}{eV} = \frac{12400\ \text{eV}\cdot\text{\AA}}{30000\ \text{eV}}. \]
Step 3: Evaluate:
\[ \lambda_{\min} = 0.4133\ \text{\AA} = 0.4133 \times 10^{-10}\ \text{m} = 41.3\ \text{pm}. \]
This matches 41.4 pm.
\[\boxed{\lambda_{\min} \approx 41.4\ \text{pm}}\]
Was this answer helpful?
0
0
Top CPET Physics Questions
- The hexadecimal equivalent of a digital number \(10011101\) is:
- If the doping concentration in a Si-Zener diode is increased, the Zener breakdown voltage:
- Which one of the following is an example of doubly magic nuclei?
- Which radiation has maximum ionization power?
- For beta-minus decay, which statement is TRUE?
View More Questions
Top CPET Nuclear physics Questions
- Which one of the following is an example of doubly magic nuclei?
- In a gamma decay process, the internal energy of the nucleus of mass \(M\) decreases, a gamma photon of energy \(E\) and linear momentum \(\dfrac{E}{c}\) is emitted, and the nucleus recoils. The decrease of internal energy is:
- An X-ray beam of wavelength \(0.16\ \text{nm}\) is incident on a set of planes of a certain crystal. The first Bragg reflection is observed for an incidence angle of \(30^\circ\). What is the corresponding interplanar spacing?
- The wavelengths of \(K_\alpha\) and \(L_\alpha\) X-rays of a material are 21.3 pm and 141 pm, respectively. Then, the wavelength of the \(K_\beta\) X-ray of the material is given by:
Top CPET Questions
- Which of the following is a key reason for choosing DRAM over SRAM for main memory?
- Which of the following components in an FPGA is responsible for implementing combinational and sequential logic?
- What is the main purpose of declaring a base class as virtual in multiple inheritance?
- What happens if a class contains at least one pure virtual function?
- What happens if a derived class defines a function with the same name as a base class function, but with a different parameter list?
View More Questions