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In an accelerator experiment on high-energy collisions of electrons with positrons, a certain event is interpreted as the annihilation of an electron-positron pair of total energy 10.2 BeV into two γ-rays of equal energy. What is the wavelength associated with each γ-ray? (1BeV = 109 eV)

1. \(3.4 \times10^{-16}\) m

2. \(1.7 \times10^{-16}\) m

3. \(2.4 \times10^{-16}\) m

4. \(3.1 \times10^{-16}\) m

Subtopic: Particle Nature of Light |

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The typical de-Broglie wavelength of an electron in metal at \(27^{\circ}\text{C}\)$$ will be:

1. | \(4.4 \times 10^{-10} ~\text{m}\) | 2. | \(3.4 \times 10^{-9}~ \text{m}\) |

3. | \(1.3 \times 10^{-10}~ \text{m}\) | 4. | \(6.2 \times 10^{-9} ~\text{m}\) |

Subtopic: De-broglie Wavelength |

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The typical de Broglie wavelength associated with a He atom in helium gas at room temperature $\left(27\xb0C\right)$ and 1 atm pressure will be:

1. \(4.63 \times 10^{-11} \mathrm{~m}\)

2. \(6.2 \times 10^{-12} \mathrm{~m}\)

3. \(7.3 \times 10^{-11} \mathrm{~m}\)

4. \(5.7 \times 10^{-12} \mathrm{~m}\)

Subtopic: De-broglie Wavelength |

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An electron microscope uses electrons accelerated by a voltage of 50 kV. The de Broglie wavelength associated with the electrons is:

1. \(6.7 \times 10^{-12} \mathrm{~m}\)

2. \(5.4 \times 10^{-12} \mathrm{~m}\)

3. \(8.5 \times 10^{-12} \mathrm{~m}\)

4. \(4.4 \times 10^{-12} \mathrm{~m}\)

Subtopic: De-broglie Wavelength |

67%

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Ultraviolet light of wavelength 2271 Å from a 100 W mercury source irradiates a photocell made of molybdenum metal. If the stopping potential is −1.3 V, the work function of the metal is:

1. 4.15 eV

2. 3.01 eV

3. 1.30 eV

4. 2.12 eV

Subtopic: Einstein's Photoelectric Equation |

60%

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Monochromatic radiation of wavelength 640.2 nm (1 nm = 10^{-9} m) from a neon lamp irradiates photosensitive material made of cesium on tungsten. The stopping voltage is measured to be 0.54 V. The source is replaced by an iron source and its 427.2 nm line irradiates the same photo-cell. The new stopping voltage is:

1. 0.54 eV

2. 1.3 eV

3. 1.5 eV

4. 1.63 eV

Subtopic: Einstein's Photoelectric Equation |

53%

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Light of intensity 10^{-5} W m^{-2} falls on a sodium photo-cell of surface area 2 cm^{2}. Assuming that the top 5 layers of sodium absorb the incident energy, The time required for photoelectric emission in the wave-picture of radiation is: (The work function for the metal is given to be about 2 eV.)

1. 0.2 year

2. 0.3 year

3. 0.4 year

4. 0.5 year

Subtopic: Einstein's Photoelectric Equation |

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The threshold frequency for a certain metal is \(3.3\times10^{14} \text{ Hz}\)$.$ If the light of frequency \(8.2\times10^{14} \text{ Hz}\) is incident on the metal, the cut-off voltage for the photoelectric emission is:

1. \(1.1210\) V

2. \(2.0292\) V

3. \(3.8651\) V

4. \(4.0832\) V

Subtopic: Einstein's Photoelectric Equation |

69%

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Light of frequency \(7.21\times 10^{14}~\text{Hz}\) is incident on a metal surface. Electrons with a maximum speed of \(6.0\times 10^{5}~\text{m/s}\) are ejected from the surface. What is the threshold frequency for the photoemission of electrons?

1. | \(5.109 \times10^{14}\) Hz | 2. | \(3.45 \times10^{14}\) Hz |

3. | \(6.733 \times10^{14}\) Hz | 4. | \(4.738 \times10^{14}\) Hz |

Subtopic: Einstein's Photoelectric Equation |

51%

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A \(100\) W sodium lamp radiates energy uniformly in all directions. The lamp is located at the center of a large sphere that absorbs all the sodium light which is incident on it. The wavelength of sodium light is \(589\) nm. What is the energy per photon associated with the sodium light?

1. \( 1.21 \) eV

2. \( 2.21 \) eV

3. \( 2.11 \) eV

4. \( 1.11\) eV

Subtopic: Particle Nature of Light |

62%

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