Dual Nature of Matter; Atoms and Nuclei

1

An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let λn, λg be the de Broglie wavelength of the electron in the nth state and the ground state respectively. Let Λn be the wavelength of the emitted photon in the transition from the nth state to the ground state. For large n, (A, B are constants)

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2

If N0 is the original mass of the substance of half-life period t1/2 = 5 years, then the amount of substance left after 15 years is

  1. N0/16
  2. N0/8
  3. N0/4
  4. N0/2
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3

If 13.6 eV energy is required to ionize the hydrogen atom, then the energy required to remove an electron from n = 2 is

  1. 0 eV
  2. 3.4 eV
  3. 6.8 eV
  4. 10.2 eV
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4

The work function of a substance is 4.0 eV. The longest wavelength of light that can cause photoelectron emission from this substance is approximately

  1. 220 nm
  2. 310 nm
  3. 400 nm
  4. 540 nm
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5

The surface of a metal is illuminated with the light of 400 nm. The kinetic energy of the ejected photoelectrons was found to be 1.68 eV. The work function of the metal is (hc = 1240 eV.nm)

  1. 1.41 eV
  2. 1.51 eV
  3. 1.68 eV
  4. 3.09 eV
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6

Energy required for the electron excitation in Li++ from the first to the third Bohr orbit is

  1. 12.1 eV
  2. 12.4 eV
  3. 36.3 eV
  4. 108.8 eV
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7

If a source of power 4 kW produces 1020 photons/second, the radiation belongs to a part of the spectrum called

  1. microwaves
  2. X rays
  3. γ rays
  4. ultraviolet rays
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8

According to Einstein’s photoelectric equation, the plot of the kinetic energy of the emitted photoelectrons from a metal vs the frequency of the incident radiation gives a straight line whose slope

  1. depends both on the intensity of the radiation and the metal used
  2. depends on the nature of the metal used
  3. depends on the intensity of the radiation
  4. is the same for all metals and independent of the intensity of the radiation
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9

At a specific instant, emission of radioactive compound is deflected in a magnetic field. The compound can emit

  1. Electrons
  2. Protons
  3. He2+
  4. Neutrons

The emission at instant can be

  1. 1, 2, 3, 4
  2. 1, 2, 3
  3. 2, 3
  4. 4
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10

Half-lives of two radioactive elements A and B are 20 minutes and 40 minutes, respectively. Initially, the samples have equal number of nuclei. After 80 minutes, the ratio of decayed numbers of A and B nuclei will be:

  1. 4 : 1
  2. 1 : 4
  3. 5 : 4
  4. 1 : 16
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