An electron of mass m with an initial velocity $\stackrel{\to }{v}={\mathrm{v}}_{0}\stackrel{^}{i}$ $$(v_o>0)$$ enters in an electric field $\stackrel{\to }{\mathrm{E}}=-{E}_{0}\stackrel{^}{i}$ (Eo = constant>0) at t=0. If ${\mathrm{\lambda }}_{0}$, is its de-Broglie wavelength initially, then what will be its de-Broglie wavelength at time t?

1. $\frac{{\mathrm{\lambda }}_{0}}{\left(1+\frac{{\mathrm{eE}}_{0}}{{\mathrm{mv}}_{0}}\mathrm{t}\right)}$

2. ${\mathrm{\lambda }}_{0}\left(1+\frac{{\mathrm{eE}}_{0}}{{\mathrm{mv}}_{0}}\mathrm{t}\right)$

3. ${\mathrm{\lambda }}_{0}\mathrm{t}$

4. ${\mathrm{\lambda }}_{0}$

Subtopic:  De-broglie Wavelength |
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When the light of frequency $$2\nu_0$$ (where $$\nu_0$$ is threshold frequency), is incident on a metal plate, the maximum velocity of electrons emitted is v1. When the frequency of the incident radiation is increased to $$5\nu_0,$$ the maximum velocity of electrons emitted from the same plate is v2. What will be the ratio of v1 to v2?
1. 1 : 2
2. 1 : 4
3. 4 : 1
4. 2 : 1

Subtopic:  Einstein's Photoelectric Equation |
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What is the de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature T (Kelvin) and mass m?

1. $\frac{h}{\sqrt{mkT}}$

2. $\frac{h}{\sqrt{3mkT}}$

3.

4. $\frac{2h}{\sqrt{mkT}}$

Subtopic:  De-broglie Wavelength |
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The photoelectric threshold wavelength of silver is 3250 x 10-10 m. What will be the velocity of the electron ejected from a silver surface by the ultraviolet light of wavelength 2536 x 10-10 m?

(Given h=  and )

1. $\approx 0.6×{10}^{6}$ ms-1
2. $\approx 61×{10}^{3}$ ms-1
3. $\approx 0.3×{10}^{6}$ ms-1
4. $$\approx 0.3\times 10^5$$ ms-1

Subtopic:  Einstein's Photoelectric Equation |
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If an electron of mass m with a de-Broglie wavelength of $$\lambda$$ falls on the target in an X-ray tube, the cut-off wavelength ( λ0) of the emitted X-ray will be:

1. ${\lambda }_{0}=\frac{2mc{\lambda }^{2}}{h}$

2. ${\lambda }_{0}=\frac{2h}{mc}$

3. ${\lambda }_{0}=\frac{2{m}^{2}{c}^{2}{\lambda }^{3}}{{h}^{2}}$

4. ${\lambda }_{0}=\lambda$

Subtopic:  De-broglie Wavelength |
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Photons with energy 5 eV are incident on a cathode C in a photoelectric cell. The maximum energy of emitted photoelectrons is 2 eV. When photons of energy 6 eV are incident on C, no photoelectron will reach the anode A, if the stopping potential of A relative to C is:

1. +3 V

2. +4 V

3. - 1V

4. -3 V

Subtopic:  Einstein's Photoelectric Equation |
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When a metallic surface is illuminated with radiation of wavelength $\lambda$, the stopping potential is V. If the same surface is illuminated with radiation of wavelength 2$\lambda$, the stopping potential is $\frac{V}{4}$ .The threshold wavelength for metallic surface is:

(a) 5$\lambda$                (b)$\frac{5}{2}$$\lambda$

(c) 3$\lambda$                (d) 4$\lambda$

Subtopic:  Photoelectric Effect: Experiment |
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An electron of mass m and a photon have the same energy E. Find the ratio of de-Broglie wavelength associated with the electron to that associated with the photon. (c is the velocity of light)

Subtopic:  De-broglie Wavelength |
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When a metallic surface is illuminated with radiation of wavelength $\mathrm{\lambda }$, the stopping potential is V. If the same surface is illuminated with radiation of wavelength 2$\mathrm{\lambda }$, the stopping potential is $\frac{V}{4}$ . The threshold wavelength for the metallic surface is:
1. 5$\mathrm{\lambda }$
2. $\frac{5}{2}\lambda$
3. 3$\mathrm{\lambda }$
4. 4$\mathrm{\lambda }$
Subtopic:  Einstein's Photoelectric Equation |
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