- 1(current)
Q. No.The ratio of wavelengths of proton and deuteron accelerated by potential \(V_{p}\) and \(V_{d}\) is \(1:\sqrt2.\) Then, the ratio of \(V_{p}\) to \(V_{d}\) will be:
1. \(1:1\)
2. \(\sqrt 2: 1\)
3. \(2:1\)
4. \(4:1\)
1. \(1:1\)
2. \(\sqrt 2: 1\)
3. \(2:1\)
4. \(4:1\)
Subtopic: De-broglie Wavelength |
Level 3: 35%-60%
JEE
Please attempt this question first.
Hints
Please attempt this question first.
Given below are two statements:
In the light of the above statements, choose the most appropriate answer from the options given below:
| Statement I: | The de Broglie wavelength associated with a material particle depends on its charge and nature. |
| Statement II: | The wave nature of particles in sub-atomic domain is significant and measurable. |
| 1. | Both Statement I and Statement II are correct. |
| 2. | Both Statement I and Statement II are incorrect. |
| 3. | Statement I is correct but Statement II is incorrect. |
| 4. | Statement I is incorrect but Statement II is correct. |
Subtopic: De-broglie Wavelength |
Level 3: 35%-60%
NEET - 2024
Hints
The de-Broglie wavelength of a photon of energy \(E\) is \(\lambda_{ph}\) and that of an electron (non-relativistic) of the same energy \(E\) is \(\lambda_{e}.\) Then (assume \(E\text ~\)few \(e\text{V}\)):
1. \(\lambda_{ph}=\lambda_e\)
2. \(\lambda_{ph}<\lambda_e\)
3. \(\lambda_{ph}>\lambda_e\)
4. any of the above may be true
1. \(\lambda_{ph}=\lambda_e\)
2. \(\lambda_{ph}<\lambda_e\)
3. \(\lambda_{ph}>\lambda_e\)
4. any of the above may be true
Subtopic: De-broglie Wavelength |
Level 3: 35%-60%
Hints
Photons of wavelength \(\lambda\) cause the emission of photoelectrons from a metallic surface, the de-Broglie wavelength of the fastest photoelectron being \(\lambda_d\). A graph of \(\dfrac{1}{\lambda} \text { vs } \dfrac{1}{\lambda_{d}}\) is:
| 1. | a straight line passing through the origin. |
| 2. | a circle. |
| 3. | an ellipse. |
| 4. | a parabola. |
Subtopic: De-broglie Wavelength |
Level 3: 35%-60%
Hints
Select the correct option based on the statements given below:
| Statement I: | By de-Broglie's hypothesis momentum of an electron, \(p=h/ \lambda\). |
| Statement II: | The energy of an electron is given by; \(E=hc/ \lambda\). |
| 1. | Statement I is correct and Statement II is incorrect. |
| 2. | Statement I is incorrect and Statement II is correct. |
| 3. | Both Statement I and Statement II are correct. |
| 4. | Both Statement I and Statement II are incorrect. |
Subtopic: De-broglie Wavelength |
52%
Level 3: 35%-60%
Hints
A particle moves in a closed orbit around the origin, due to a force which is directed toward the origin. The de-Broglie wavelength of the particle varies cyclically between the two values \(\lambda_{1} , \lambda_{2}\) with \(\lambda_{1} > \lambda_{2}.\) Which of the following statement/s is/are true?
| (a) | The particle could be moving in a circular orbit with the origin as the centre. |
| (b) | The particle could be moving in an elliptic orbit with origin as its focus. |
| (c) | When the de-Broglie wavelength is \(λ_1,\) the particle is nearer the origin than when its value is \(λ_2.\) |
| (d) | When the de-Broglie wavelength is \(λ_2,\) the particle is nearer the origin than when its value is \(λ_1.\) |
Choose the correct option from the given ones:
| 1. | (b) and (d) only |
| 2. | (a) and (c) only |
| 3. | (b), (c), and (d) only |
| 4. | (a), (c), and (d) only |
Subtopic: De-broglie Wavelength |
50%
Level 3: 35%-60%
Hints
Relativistic corrections become necessary when the expression for the kinetic energy \(\dfrac{1}{2} mv^{2}\), becomes comparable with \(mc^{2}\), where \(m\) is the mass of the particle. At what de-Broglie wavelength, will relativistic corrections become important for an electron?
| (a) | \(\lambda = 10~\text{nm}\) | (b) | \(\lambda = 10^{-1}~\text{nm}\) |
| (c) | \(\lambda = 10^{- 4}~\text{nm}\) | (d) | \(\lambda = 10^{- 6}~\text{nm}\) |
Choose the correct option:
1. (a), (c)
2. (a), (d)
3. (c), (d)
4. (a), (b)
Subtopic: De-broglie Wavelength |
53%
Level 3: 35%-60%
Hints
A nucleus of mass \(M,\) initially at rest, splits into two fragments with masses \(\dfrac{M'}{ 3}\) and \(\dfrac{2M'} { 3}\) \((M'<M).\) The ratio of the de-Broglie wavelengths of the two fragments is:
| 1. | \(1:2\) | 2. | \(2:1\) |
| 3. | \(1:1\) | 4. | \(2:3\) |
Subtopic: De-broglie Wavelength |
56%
Level 3: 35%-60%
JEE
Please attempt this question first.
Hints
Please attempt this question first.
The graph that shows the variation of \({\dfrac{1}{\lambda^2}}\) with the kinetic energy \(E\) (where \(\lambda\) is the de-Broglie wavelength of a free particle) is:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: De-broglie Wavelength |
57%
Level 3: 35%-60%
NEET - 2024
Hints
The de-Broglie wavelength associated with an electron, accelerated by a potential difference of \(81\) V is given by:
1. \(13.6\) nm
2. \(136\) nm
3. \(1.36\) nm
4. \(0.136\) nm
1. \(13.6\) nm
2. \(136\) nm
3. \(1.36\) nm
4. \(0.136\) nm
Subtopic: De-broglie Wavelength |
58%
Level 3: 35%-60%
NEET - 2023
Hints
- 1(current)
Q. No.
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