Summary of HC Verma Solutions Part 2 Chapter 44: X-Rays
FAQs on HC Verma Solutions Class 12 Chapter 44 - X Rays
1. How can Vedantu's solutions for HC Verma Class 12 Chapter 44 help in my board and competitive exam preparation?
Vedantu's solutions for HC Verma's 'X-Rays' chapter provide detailed, step-by-step explanations for every problem. This helps in building a strong conceptual foundation beyond the standard syllabus, which is crucial for competitive exams like JEE and NEET. By mastering these solutions, you can handle complex numericals on topics like Bragg's Law and Moseley's Law, improving both your problem-solving speed and accuracy.
2. What is the step-by-step method to solve problems on the cutoff wavelength of X-rays using the Duane-Hunt law in HC Verma?
To solve for the cutoff wavelength (λ_min) using the Duane-Hunt law, follow these steps:
- First, identify the accelerating voltage (V) applied to the Coolidge tube from the problem statement.
- The maximum energy of a photon (E_max) is equal to the kinetic energy of the electron, which is E_max = eV, where 'e' is the charge of an electron.
- Use the formula E = hc/λ, where 'h' is Planck's constant and 'c' is the speed of light.
- Combine the two to get the Duane-Hunt formula: λ_min = hc / eV.
- Substitute the values of h, c, e, and V to calculate the minimum wavelength.
3. How is Bragg's Law applied to solve numericals on X-ray diffraction in Chapter 44?
Bragg's Law is fundamental for solving problems involving X-ray diffraction by a crystal lattice. The law is given by 2d sin(θ) = nλ. To apply it:
- Identify the given variables: interplanar spacing (d), the angle of incidence (θ), and the order of diffraction (n).
- The problem will typically ask you to find the wavelength (λ) of the X-rays or the spacing (d).
- Ensure the angle θ is the glancing angle, not the angle of incidence with the normal.
- For the first-order maximum, use n=1. Substitute the known values into the equation and solve for the unknown variable.
4. How is Moseley's Law used to identify elements from their characteristic X-ray spectra in HC Verma problems?
Moseley's Law relates the frequency (ν) of characteristic X-rays to the atomic number (Z) of the target element. The formula is √ν = a(Z - b), where 'a' and 'b' are constants. To identify an element:
- You will typically be given the wavelength or frequency of a specific spectral line (like Kα).
- Use the formula to calculate the atomic number (Z). The constant 'b' is the screening constant, which is approximately 1 for K-series X-rays.
- Once you find the value of Z, you can identify the element from the periodic table. This method is a powerful tool for elemental analysis problems in the chapter.
5. What is the key difference between continuous and characteristic X-rays, and how does this affect the approach to solving problems in HC Verma Chapter 44?
The primary difference lies in their origin. Continuous X-rays (or Bremsstrahlung) are produced when high-speed electrons are decelerated by the target nucleus, resulting in a continuous spectrum of wavelengths down to a minimum cutoff value (λ_min). Problems involving continuous X-rays often use the Duane-Hunt law (λ_min = hc/eV). In contrast, characteristic X-rays are produced when an electron knocks out an inner-shell electron of a target atom, and an outer-shell electron fills the vacancy, emitting a photon of a specific, discrete energy. Problems on characteristic X-rays require the use of Moseley's Law and energy level transitions.
6. Why is the concept of a Coolidge tube important for solving problems related to the intensity and energy of X-rays in this chapter?
The Coolidge tube is the experimental setup for producing X-rays, and understanding its components is crucial for problem-solving.
- The accelerating voltage (V) between the cathode and anode determines the maximum kinetic energy of the electrons and thus the minimum wavelength (or maximum energy) of the continuous X-ray spectrum.
- The filament current controls the temperature of the filament, which in turn determines the number of electrons emitted per second. This directly affects the intensity (number of X-ray photons) produced, but not their maximum energy.
Distinguishing between these two controls is key to correctly interpreting and solving HC Verma problems on X-ray production.
7. How do the problems on X-rays in HC Verma differ in difficulty and scope from those typically found in NCERT textbooks for Class 12 Physics?
Problems in HC Verma on X-rays are generally more analytical and conceptually demanding than those in NCERT. While NCERT focuses on introducing the basic laws like Bragg's Law and Moseley's Law, HC Verma challenges students to:
- Apply these laws in more complex, multi-step scenarios.
- Integrate concepts from previous chapters, such as electromagnetism and modern physics.
- Analyse the working of the Coolidge tube in greater detail, linking its parameters to the output X-ray beam's properties.
This approach makes HC Verma essential for building the advanced problem-solving skills required for competitive examinations like JEE and NEET.
