The wavelength of a photon needed to remove a proton from a nucleus which is bound to the nucleus with 1 MeV energy is nearly

1

(a)

1.2 nm

(b)

1.2x\({ 10 }^{ -3 }\)nm

(c)

1.2x\({ 10 }^{ -6 }\)nm

(d)

1.2x\({ 10 }^{ 1 }\)nm

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

1

(a)

remains constant

 

 

(b)

increases with time.

(c)

decreases with time.

(d)

increases and decreases periodically.

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

1

(a)

\({ \lambda }_{ 0 }\)

(b)

 \({ \lambda }_{ 0 }\sqrt { 1+\frac { { e }^{ 2 }{ E }_{ 0 }^{ 2 }\quad { t }^{ 2 } }{ { m }^{ 2 }{ v }_{ 0 }^{ 2 } } } \)

(c)

\(\frac { { \lambda }_{ 0 } }{ \sqrt { 1+\frac { { e }^{ 2 }{ E }^{ 2 }{ t }^{ 2 } }{ { m }^{ 2 }{ { v }_{ 0 }^{ 2 } } } } } \)

(d)

\(\frac { { \lambda }_{ 0 } }{ \sqrt { 1+\frac { { e }^{ 2 }{ E }^{ 2 }{ t }^{ 2 } }{ { m }^{ 2 }{ { v }_{ 0 }^{ 2 } } } } } \)

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?

1

(a)

\(\lambda =10nm\)     

(b)

 \(\lambda ={ 10 }^{ -1 }nm\)

(c)

\(\lambda ={ 10 }^{ -4 }nm\)       

(d)

\(\lambda ={ 10 }^{ -6 }nm\)

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

(a)

Lithium, because its work function is less than the energy of the visible light photons.

It is harder to remove a free electron from copper than from sodium. Which has higher work function?

1

(a)

The work function of copper is higher than that of sodium.

An electron and photon possessing same K.E. Which one will have greater wavelength?

1

(a)

1/2 mv² = (m²v²)/2m = p₂/2m
According to De Broglie wave length \(\lambda \) = h/p
\(\lambda \)_e/\(\lambda \)_p = P_p/P_e = \(\surd \)(m_p/m_e)
m_e < m_p
\(\lambda \)_e > \(\lambda \)_p
electrons have greater De broglie wavelength than proton

In Davisson – Germer experiment if the angle of diffraction is 520 find Glancing angle?

1

(a)

\(\theta\) = 90 - \(\phi \)/2
= 90 - 52/2 = 64⁰

What is the energy associated with a photon of wavelength 6000 A⁰ ?

1

(a)

E = hc/ \(\lambda \)
= 3.3 x 10^-19 J