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Published on: 28/08/2019
Dual Nature of Radiation and Matter
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Questions + Answers key
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1.
Relativistic corrections become necessary when the expression for the kinetic energy \(\frac { 1 }{ 2 } m{ v }^{ 2 }\) becomes comparable with \(m{ c }^{ 2 }\) where m is the mass of the particle. At what de-Broglie wavelength will relativistic corrections become important for an electron?
\(\lambda =10nm\)
\(\lambda ={ 10 }^{ -1 }nm\)
\(\lambda ={ 10 }^{ -4 }nm\)
\(\lambda ={ 10 }^{ -6 }nm\)
2.
An electron (mass m) with an initial velocity \(v={ v }_{ 0 }\vec { i } \) is in an electric field \(E={ E }_{ 0 }\vec { j } E={ E }_{ 0 }\vec { j } \) . If \(\lambda =\frac { h }{ m{ v }_{ 0 } } \) its de-Broglie wavelength at time t is given by
\({ \lambda }_{ 0 }\)
\({ \lambda }_{ 0 }\sqrt { 1+\frac { { e }^{ 2 }{ E }_{ 0 }^{ 2 }\quad { t }^{ 2 } }{ { m }^{ 2 }{ v }_{ 0 }^{ 2 } } } \)
\(\frac { { \lambda }_{ 0 } }{ \sqrt { 1+\frac { { e }^{ 2 }{ E }^{ 2 }{ t }^{ 2 } }{ { m }^{ 2 }{ { v }_{ 0 }^{ 2 } } } } } \)
\(\frac { { \lambda }_{ 0 } }{ \sqrt { 1+\frac { { e }^{ 2 }{ E }^{ 2 }{ t }^{ 2 } }{ { m }^{ 2 }{ { v }_{ 0 }^{ 2 } } } } } \)
3.
An electron is moving with an initial velocity \(\frac { h }{ mv } ={ v }_{ 0 }\overset { \wedge }{ L } \) and is in a magnetic field \(\vec { B= } \ { B }_{ 0 }\vec { j } \) Then its de-Broglie wavelength
remains constant
increases with time.
decreases with time.
increases and decreases periodically.
4.
What is the energy associated with a photon of wavelength 6000 A0 ?
5.
In Davisson – Germer experiment if the angle of diffraction is 520 find Glancing angle?
6.
An electron and photon possessing same K.E. Which one will have greater wavelength?
7.
It is harder to remove a free electron from copper than from sodium. Which has higher work function?
8.
The work function of lithium and copper are 2.3eV and 4.0eV respectively. Which of these metals will be useful for the photoelectric cell working with visible light? Explain.
1.
(d)
\(\lambda ={ 10 }^{ -6 }nm\)
2.
(c)
\(\frac { { \lambda }_{ 0 } }{ \sqrt { 1+\frac { { e }^{ 2 }{ E }^{ 2 }{ t }^{ 2 } }{ { m }^{ 2 }{ { v }_{ 0 }^{ 2 } } } } } \)
3.
(a)
remains constant
4.
\(E=h c / \lambda\)
= 3.3 x 10-19 J
5.
\(\theta=90-\phi / 2\)
\(=90-52 / 2=64^{\circ}\)
6.
\(1 / 2 m v^2=\left(m^2 v^2\right) / 2 m=p_2 / 2 m\)
According to De Broglie wave length \(\lambda=h / p\)
\(
\lambda_e / \lambda_p=P_p / P_e=\sqrt{ }\left(m_p / m_e\right) \\
m_e<m_p \\
\lambda_e>\lambda_p
\)
electrons have greater De broglie wavelength than proton
7.
The work function of copper is higher than that of sodium.
8.
Lithium, because its work function is less than the energy of the visible light photons.
12th Standard CBSE Syllabus & Materials
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