Home
Class 12
PHYSICS
If the potential difference of coolidge ...

If the potential difference of coolidge tube probucing X-ray is increased, then choose the corrent option (s).
Here, `lambda_0` is cut off wavelength and `lambda_(Ka) and lambda_(K beta)` are wavelengths of `K_(alpha) and K_(beta)` characteristic X-rays.

A

the interval between `lambda_(Kalpha)` and `lambda_(Kbeta) ` increases

B

the interval between `lambda_(Kalpha)` and `lambda_0 ` increases

C

the interval between `lambda_(Kbeta)` and `lambda_0 ` increases

D

`lambda_0` does not change

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze how the increase in potential difference (V) in a Coolidge tube affects the wavelengths of the emitted X-rays, specifically the cut-off wavelength (λ₀) and the characteristic wavelengths (λₖₐ and λₖβ). ### Step-by-Step Solution: 1. **Understanding the Cut-off Wavelength (λ₀)**: The cut-off wavelength (λ₀) is given by the formula: \[ λ₀ = \frac{hc}{eV} \] where: - \(h\) is Planck's constant, - \(c\) is the speed of light, - \(e\) is the charge of an electron, - \(V\) is the potential difference. 2. **Effect of Increasing Potential Difference (V)**: From the formula, we can see that λ₀ is inversely proportional to the potential difference (V). This means: - If \(V\) increases, then \(λ₀\) decreases. 3. **Analyzing the Wavelengths of Characteristic X-rays**: The characteristic X-ray wavelengths (λₖₐ and λₖβ) are specific to the material and are not directly affected by the potential difference. However, the intervals between these wavelengths and λ₀ will change as λ₀ changes. 4. **Interval Between Wavelengths**: - The interval between λₖₐ and λ₀ is given by: \[ \text{Interval}_{kα} = λₖₐ - λ₀ \] Since λ₀ decreases, this interval increases. - The interval between λₖβ and λ₀ is given by: \[ \text{Interval}_{kβ} = λₖβ - λ₀ \] Similarly, since λ₀ decreases, this interval also increases. 5. **Conclusion**: - The interval between λₖₐ and λₖβ does not change because the characteristic wavelengths are fixed for a given material. - The intervals between λₖₐ and λ₀, and λₖβ and λ₀ both increase due to the decrease in λ₀. ### Correct Options: - The interval between λₖₐ and λ₀ increases (Correct). - The interval between λₖβ and λ₀ increases (Correct). - The interval between λₖₐ and λₖβ does not change (Incorrect). - λ₀ does change (Incorrect). ### Final Answer: The correct options are: - The interval between λₖₐ and λ₀ increases. - The interval between λₖβ and λ₀ increases.

To solve the problem, we need to analyze how the increase in potential difference (V) in a Coolidge tube affects the wavelengths of the emitted X-rays, specifically the cut-off wavelength (λ₀) and the characteristic wavelengths (λₖₐ and λₖβ). ### Step-by-Step Solution: 1. **Understanding the Cut-off Wavelength (λ₀)**: The cut-off wavelength (λ₀) is given by the formula: \[ λ₀ = \frac{hc}{eV} ...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • MODERN PHYSICS - 1

    DC PANDEY ENGLISH|Exercise Level 2 Comprehension Based|3 Videos
  • MODERN PHYSICS - 1

    DC PANDEY ENGLISH|Exercise Level 2Passage 2|1 Videos
  • MODERN PHYSICS - 1

    DC PANDEY ENGLISH|Exercise Level 2 Single Correct|22 Videos
  • MODERN PHYSICS

    DC PANDEY ENGLISH|Exercise Integer Type Questions|17 Videos
  • MODERN PHYSICS - 2

    DC PANDEY ENGLISH|Exercise Level 2 Subjective|10 Videos

Similar Questions

Explore conceptually related problems

Let lambda_(alpha), lambda_(beta),and lambda'_(alpha) denote the wavelength of the X-ray of the K_(alpha), K_(beta), and L_(alpha) lines in the characteristic X-rays for a metal. Then.

Let lambda_(alpha'), lambda_(beta),and lambda'_(alpha) denote the wavelength of the X-ray of the K_(alpha), K_(beta), and L_(alpha) lines in the characteristic X-rays for a metal. Then.

If lambda_(min) is minimum wavelength produced in X-ray tube and lamda_(kalpha) is the wavelength of K_(alpha) line. As the operating tube voltage is increased.

An X-ray tube is operated at 20 kV. The cut off wavelength is

The operating potential in an x-ray tube is increased by 2%. The percentage change in the cut off wavelength is

In a Coolidge tube, the potential difference used to accelerate the electrons is increased from 12.4 kV to 24.8 kV . As a result, the difference between the wavelengths of K_(alpha) -line and minimum wavelength becomes thrice. The wavelength of the K_(alpha) line is 0.25xxKA^(@) . Find the value of K . (hc)/(e)=(12.4 KVA^(@))

The intensity of X- ray from a coolidge tube is plotted againest wavelength lambda as shown in the figure . The minimum wavelength found lambda_(c) and the wavelength of the k_(a) line is lambda_(k) , As the accelerating voliage is increase

A potential difference of 20 kV is applied across an X-ray tube. The minimum wavelength of X-rays generated (in angstrom) is :-

In X-ray spectrum wavelength lamda of line K_(alpha) depends on atomic number Z as

The intensity of X-rays form a Coolidge tube is plotted against wavelength lambda as shown in the figure. The minimum wavelength found is lambda_c and the wavelength of the K_(alpha) line is lambda_k . As the accelerating voltage is increased (a) lambda_k - lambda_c increases (b) lambda_k - lambda_c decreases (c ) lambda_k increases (d) lambda_k decreases