Photoelectrons emerging from a photocathode (work function: $2.2~\text{eV}$ ) are allowed to fall onto a gas containing hydrogen atoms in the ground state and the first excited state. What is the minimum energy of the photons incident on the photo-cathode that will cause the photoelectrons to transfer energy to the $\mathrm{H\text-}$ atoms?

1. $13.6~\text{eV}+2.2~\text{eV}$

2. $(10.2+2.2)~\text{eV}$

3. $(3.4+2.2)~\text{eV}$

4. $(1.89+2.2)~\text{eV}$

Subtopic: Photoelectric Effect: Experiment |

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Q11:

A photon of energy

$E_p$ has the same wavelength as an electron of kinetic energy

$E_e.$ The rest energy (i.e.,

$mc^2$ ) of the electron is:
1.

$\dfrac{E^2_p}{E_e}$

2.

$\dfrac{E^2_e}{E_p}$

3.

$\dfrac{E^2_e}{2E_p}$

4.

$\dfrac{E^2_p}{2E_e}$

Subtopic: De-broglie Wavelength |

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Q12:

Ultraviolet photons, each of energy

$20~\text{eV},$ are incident onto a gas of

$\mathrm {H}$ -atoms, causing the emission of electrons. The kinetic energy of the emitted electrons has the value:
1.

$6.4~\text{eV}$
2.

$7.2~\text{eV}$
3.

$3.2~\text{eV}$
4.

$13.6~\text{eV}$

Subtopic: Electron Emission |

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Q13:

The de-Broglie wavelength of the electron accelerated through a potential difference

$V$ equals the de-Broglie wavelength of an electron in the ground state of the hydrogen atom. The value of

$V$ is:
1.

$13.6$ volts
2.

$27.2$ volts
3.

$10.2$ volts
4.

$6.8$ volts

Subtopic: De-broglie Wavelength |

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Q14:

The de-Broglie wavelength of a photon of energy

$E$ is

$\lambda_{ph}$ and that of an electron (non-relativistic) of the same energy

$E$ is

$\lambda_{e}.$ Then (assume

$E\text ~$ few

$e\text{V}$ ):
1.

$\lambda_{ph}=\lambda_e$
2.

$\lambda_{ph}<\lambda_e$
3.

$\lambda_{ph}>\lambda_e$
4. any of the above may be true

Subtopic: De-broglie Wavelength |

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Q15:

A hydrogen atom

$(\mathrm{H})$ and a helium

$(\mathrm{He})$ atom, both have the same kinetic energy (they are non-relativistic). Their de-Broglie wavelengths are in the ratio:

$\Large\frac{\lambda_\mathrm{H}}{\lambda_{\mathrm{He}}}=$

1.	$4$	2.	$\dfrac14$
3.	$2$	4.	$\dfrac12$

Subtopic: De-broglie Wavelength |

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Q16:

In an experiment on the photoelectric effect, the maximum kinetic energy of the emitted electrons is plotted as a function of the frequency of incident radiation. The graph is:

1.	a straight line with a positive intercept on the $x$ -axis (frequency)
2.	a straight line with a positive intercept on the $y$ -axis (kinetic energy)
3.	a parabola
4.	a hyperbola

Subtopic: Photoelectric Effect: Experiment |

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Q17:

Which, of the following, shows the correct graph of the de-Broglie wavelength

$(\lambda)$ of a particle and its kinetic energy

$(E_K)?$

1.		2.
3.		4.

Subtopic: De-broglie Wavelength |

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Q18:

Select the correct option based on the statements given below:

Statement I:	By de-Broglie's hypothesis momentum of an electron, $p=h/ \lambda$ .
Statement II:	The energy of an electron is given by; $E=hc/ \lambda$ .

1.	Statement I is correct and Statement II is incorrect.
2.	Statement I is incorrect and Statement II is correct.
3.	Both Statement I and Statement II are correct.
4.	Both Statement I and Statement II are incorrect.

Subtopic: De-broglie Wavelength |

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Q19:

Photons and electrons of the same wavelength are compared. Which one carries larger momentum?

1.	photon
2.	electron
3.	neither, since both have equal momenta
4.	it could be either, depending on the energy

Subtopic: De-broglie Wavelength |

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1.	$13.6~\text{eV}+2.2~\text{eV}$
2.	$(10.2+2.2)~\text{eV}$
3.	$(3.4+2.2)~\text{eV}$
4.	$(1.89+2.2)~\text{eV}$

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