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. \(4:1\) 
Subtopic:  De-broglie Wavelength |
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Given below are two statements:
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.
In the light of the above statements, choose the most appropriate answer from the options given below:
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 |
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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
Subtopic:  De-broglie Wavelength |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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
Subtopic:  De-broglie Wavelength |
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