Relativistic corrections become necessary when the expression for the kinetic energy 12mv2, becomes comparable with mc2, where m is the mass of the particle. At what de-Broglie wavelength, will relativistic corrections become important for an electron?

(a) λ=10 nm
(b) λ=10-1 nm
(c) λ=10-4 nm
(d) λ=10-6 nm

1. (a, c)

2. (a, d)

3. (c, d)

4. (a, b)

Subtopic:  De-broglie Wavelength |
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An electron (mass m) with an initial velocity v=v0i^ is in an electric field E=E0j^. If λ0=hmv0, its de-Broglie wavelength at time t is given by:

1. λ0

2. λ01+e2E02t2m2v02

3. λ01+e2E02t2m2v02

4. λ01+e2E02t2m2v02

Subtopic:  De-broglie Wavelength |
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An electron (mass \(m\)) with an initial velocity \(\overrightarrow{\mathrm{v}}=\mathrm{v}_0 \hat{\mathrm{i}}\) (\(\mathrm{v}_0>0\)is in an electric field \(\overrightarrow{\mathrm{E}}=-\mathrm{E}_0 \hat{\mathrm{i}}\)(\(E_o\)=constant\(>0\)). Its de-Broglie wavelength at time \(t\) is given by:

1. \(\frac{\lambda_0}{\left(1+\frac{e E_0}{m} \frac{t}{\mathrm{v}_0}\right)}\) 2. \(\lambda_0\left(1+\frac{e E_0 t}{m \mathrm{v}_0}\right)\)
3. \(\lambda_0 \) 4. \(\lambda_0t\)
Subtopic:  De-broglie Wavelength |
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An electron is moving with an initial velocity v=v0i^ and is in a magnetic field B=B0j^. Then, its de-Broglie wavelength:

1. remains constant

2. increases with time

3. decreases with time

4. increases and decreases periodically

Subtopic:  De-broglie Wavelength |
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A proton, a neutron, an electron and an α-particle have the same energy. Then, their de-Broglie wavelengths compare as:

1. λp=λn>λe>λα

2. λα<λp=λn<λe

3. λe<λp=λn>λα

4. λe=λp=λn=λα

Subtopic:  De-broglie Wavelength |
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Two particles \(A_1\) and \(A_2\) of masses \({m_1},m_2\)  \(({m_1>m_2})\) have the same de-Broglie wavelength. Then:

(a) their momenta (magnitude) are the same
(b) their energies are the same
(c) energy of \(A_1\) is less than the energy of \(A_2\)
(d) energy of \(A_1\) is more than the energy of \(A_2\)

1. (b), (c)
2. (a), (c)
3. (c), (d)
4. (b), (d)

Subtopic:  De-broglie Wavelength |
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The de-Broglie wavelength of a photon is twice the de-Broglie wavelength of an electron. The speed of the electron is ve=c100. Then,

1. \(\frac{E_e}{E_p}=10^{-4}\)

2. \(\frac{E_e}{E_p}=10^{-2}\)

3. \(\frac{P_e}{m_ec}=10^{-2}\)

4. \(\frac{P_e}{m_ec}=10^{-4}\)

Subtopic:  De-broglie Wavelength |
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Photons absorbed in matter are converted to heat. A source emitting n photon/sec of frequency ν is used to convert 1 kg of ice at 0°C to water at 0°C. Then, the time T taken for the conversion:
 

(a) decreases with increasing n, with  ν fixed
(b) decreases with n fixed,  ν increasing
(c) remains constant with n and  ν changing such that n ν =constant
(d) increases when the product n ν increases



1. (b, d)
2. (a, c, d)
3. (a, d)
4. (a, b, c)

Subtopic:  Particle Nature of Light |
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A particle moves in a closed orbit around the origin, due to a force which is directed towards the origin. The de-Broglie wavelength of the particle varies cyclically between two values λ1, λ2 with λ1>λ2. Which of the following statement/s is/are true?

(a) The particle could be moving in a circular orbit with 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 .

1. (b, d)

2. (a, c)

3. (b, c, d)

4. (a, c, d)

Subtopic:  De-broglie Wavelength |
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Consider a beam of electrons (each electron with energy \(E_0\)) incident on a metal surface kept in an evacuated chamber. Then:

1. no electrons will be emitted as only photons can emit electrons.
2. electrons can be emitted but all with energy, \(E_0\).
3. electrons can be emitted with any energy, with a maximum of \(\mathrm{E}_0-\phi\) (\(\phi\) is the work function).
4. electrons can be emitted with any energy, with a maximum \(E_0\).
Subtopic:  Electron Emission |
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