Q. No.The de-Broglie wavelength associated with an electron accelerated through a potential difference \(V\) is \(\lambda_e\) \(\lambda_p.\) \(m_e\) \(m_p,\)
1. \(\sqrt{\dfrac{m_p}{m_e}} \)
2. \( \sqrt{\dfrac{m_e}{m_p}}\)
3. \(\dfrac{m_p}{m_e}\)
4. \(\left(\dfrac{m_p}{m_e}\right)^2\)
1. \(\sqrt{\dfrac{m_p}{m_e}} \)
2. \( \sqrt{\dfrac{m_e}{m_p}}\)
3. \(\dfrac{m_p}{m_e}\)
4. \(\left(\dfrac{m_p}{m_e}\right)^2\)
Subtopic: De-broglie Wavelength |
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The de-Broglie wavelength for an electron accelerated through the potential difference of \(V_1\)
1. \(4\)
2. \(3\)
3. \(2\)
4. \(1\)
1. \(4\)
2. \(3\)
3. \(2\)
4. \(1\)
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An electron of mass \(m\) is moving in an electric field \(\vec{E}=-2 E_{0} \hat{i}\left(E_{0}=\text { constant }>0\right),\) with an initial velocity \(v_{0} \hat{i}\)
\(\left(v_{0}=\text { constant }>0\right). \text { If } \lambda_{0}=\dfrac{h}{4 m v_{{0}}},\) its de Broglie wavelength at time \(t\) is:
(\(e\) = charge of electron)
1. \(\dfrac{4 \lambda_{{0}}}{\left[1-\dfrac{E_{{0}} e}{2 m} \dfrac{t}{v_{{0}}}\right]}\)
2. \(\dfrac{4 \lambda_{0}}{\left[1+\dfrac{E_{0} e}{2 m} \dfrac{t}{v_{0}}\right]}\)
3. \(\dfrac{4 \lambda_{0}}{\left[1+\dfrac{2 E_{{0}} e}{m} \dfrac{t}{v_{{0}}}\right]}\)
4. \(\dfrac{4 \lambda_{0}}{\left[1-\dfrac{2 E_{0} e}{m} \dfrac{t}{v_{0}}\right]}\)
\(\left(v_{0}=\text { constant }>0\right). \text { If } \lambda_{0}=\dfrac{h}{4 m v_{{0}}},\) its de Broglie wavelength at time \(t\) is:
(\(e\) = charge of electron)
1. \(\dfrac{4 \lambda_{{0}}}{\left[1-\dfrac{E_{{0}} e}{2 m} \dfrac{t}{v_{{0}}}\right]}\)
2. \(\dfrac{4 \lambda_{0}}{\left[1+\dfrac{E_{0} e}{2 m} \dfrac{t}{v_{0}}\right]}\)
3. \(\dfrac{4 \lambda_{0}}{\left[1+\dfrac{2 E_{{0}} e}{m} \dfrac{t}{v_{{0}}}\right]}\)
4. \(\dfrac{4 \lambda_{0}}{\left[1-\dfrac{2 E_{0} e}{m} \dfrac{t}{v_{0}}\right]}\)
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An electron is travelling with a velocity \(v\) in free space and when it enters a medium, its velocity is reduced by \(20 \%\). The de Broglie wavelength of electron in the medium is \(\alpha \lambda_{0},\) where \(\lambda_0\)
1. \(1.20\)
2. \(1.0 \)
3. \(1.25\)
4. \(0.75\)
1. \(1.20\)
2. \(1.0 \)
3. \(1.25\)
4. \(0.75\)
Subtopic: De-broglie Wavelength |
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A particle having electric charge \(3\times 10^{-19}~\text{C}\) and mass \(6\times 10^{-27}~\text{kg}\) is accelerated by applying an electric potential of \(1.21~\text{V}\). Wavelength of the matter wave associated with the particle is \(\alpha\times 10^{-12}~\text{m}.\) The value of \(\alpha\) is:
(Take Planck’s constant \(= 6.6\times 10^{-34}~\text{J.s}\))
1. \(10\)
2. \(15\)
3. \(20\)
4. \(25\)
(Take Planck’s constant \(= 6.6\times 10^{-34}~\text{J.s}\))
1. \(10\)
2. \(15\)
3. \(20\)
4. \(25\)
Subtopic: De-broglie Wavelength |
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The de-Broglie wavelength of an oxygen molecule at \(27^{\circ}\text{C}\) is \(x\times 10^{-12}\) m. The value of \(x\) is: (take Planck's constant = \(6.63\times 10^{-34}~\text{J.s}\), Boltzmann constant = \(1.38\times 10^{-23}\) J/K, mass of oxygen molecule = \(5.31\times 10^{-26}\) kg).
1. \(26\)
2. \(24\)
3. \(30\)
4. \(20\)
1. \(26\)
2. \(24\)
3. \(30\)
4. \(20\)
Subtopic: De-broglie Wavelength |
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The ratio of de-Broglie wavelength of a deutron with kinetic energy \(E\) to that of an alpha particle with kinetic energy \(2E\) is \(n:1\). The value of \(n\) is:
(Assume mass of proton = mass of neutron)
1. \(5\)
2. \(3\)
3. \(2\)
4. \(1\)
(Assume mass of proton = mass of neutron)
1. \(5\)
2. \(3\)
3. \(2\)
4. \(1\)
Subtopic: De-broglie Wavelength |
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An electron is released from rest near an infinite non-conducting sheet of uniform charge density \(\text-σ. \) The rate of change of de-Broglie wavelength associated with the electron varies inversely as \(n^\text{th} \) power of time. The numerical value of \(n\) is:
1. \(3\)
2. \(2\)
3. \(5\)
4. \(9\)
1. \(3\)
2. \(2\)
3. \(5\)
4. \(9\)
Subtopic: De-broglie Wavelength |
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A photo emissive substance is illuminated with a radiation of wavelength \(λ_i,\) so that it releases electrons with de-Broglie wavelength \(λ_e.\) The longest wavelength of radiation that can emit photoelectron is \(λ_0. \) Expression for de-Broglie wavelength is given by:
(\(m:\) mass of the electron, \(h:\) Planck's constant and \(c:\) speed of light)
(\(m:\) mass of the electron, \(h:\) Planck's constant and \(c:\) speed of light)
| 1. | \(\lambda_e=\sqrt{\dfrac{h \lambda_0}{2 m c}} \) |
| 2. | \(\lambda_{\mathrm{e}}=\dfrac{{h}}{\sqrt{2 {mc}\left(\dfrac{1}{\lambda_i}-\dfrac{1}{\lambda_0}\right)}} \) |
| 3. | \(\lambda_e=\sqrt{\dfrac{h \lambda_i}{2 m c}} \) |
| 4. | \(\lambda_{{e}}=\sqrt{\dfrac{{h}}{2 {mc}\left(\dfrac{1}{\lambda_i}-\dfrac{1}{\lambda_{{0}}}\right)}} \) |
Subtopic: De-broglie Wavelength |
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An electron with mass m with an initial velocity \((t=0) \vec{v}=v_0 \hat{\imath}\left(v_0>0\right)\) enters a magnetic field \(\vec{B}=B_0 \hat{\jmath} .\) If the initial de-Broglie wavelength at \(t=0\) is \(\lambda _0,\) then its value after time \(t\) would be:
1. \(\lambda_0\)
2. \(\dfrac{\lambda_0}{\sqrt{1-\dfrac{{e}^2 {B}_0^2 {t}^2}{{m}^2}}}\)
3. \(\lambda_0 \sqrt{1+\dfrac{{e}^2 {B}_0^2 {t}^2}{{m}^2}} \)
4. \(\dfrac{\lambda_0}{\sqrt{1+\dfrac{{e}^2{B}_0^2 {t}^2}{{m}^2}}} \)
1. \(\lambda_0\)
2. \(\dfrac{\lambda_0}{\sqrt{1-\dfrac{{e}^2 {B}_0^2 {t}^2}{{m}^2}}}\)
3. \(\lambda_0 \sqrt{1+\dfrac{{e}^2 {B}_0^2 {t}^2}{{m}^2}} \)
4. \(\dfrac{\lambda_0}{\sqrt{1+\dfrac{{e}^2{B}_0^2 {t}^2}{{m}^2}}} \)
Subtopic: De-broglie Wavelength |
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