Atom, Origin of Spectra: Bohr's Theory of Hydrogen Atom — Practice Quiz
ICSE · Class 12 · Physics
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Quick Quiz: Atom, Origin of Spectra: Bohr's Theory of Hydrogen Atom
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A muonic hydrogen atom has a ground-state radius of 2.56 × 10^-13 m. How many times smaller is this radius than the ground-state radius of ordinary hydrogen, 0.53 Å?
An alpha particle of charge +2e is accelerated through a potential difference of 2.0 × 10^6 V. What is its kinetic energy on reaching a gold foil?
A gold nucleus has atomic number 79. For an alpha particle with kinetic energy 1.48 × 10^-12 J, what is the distance of closest approach r0? Use r0 = (1/4πε0)(2Ze^2/K) and 1/4πε0 = 9.0 × 10^9 N m^2 C^-2.
For a hydrogen atom, what is the radius of the second Bohr orbit? Use r1 = 0.53 Å and rn = (0.53)n^2 Å for hydrogen.
Sample Questions
In a hydrogen-like atom with atomic number Z = 3, what is the radius of the third orbit? Use rn = (0.53)n^2/Z Å.
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1.59 Å
Use rn = (0.53)n^2/Z Å. For n = 3 and Z = 3, r3 = 0.53 × 9 / 3 = 1.59 Å.
For hydrogen, what is the speed of the electron in the second Bohr orbit if the speed in the first orbit is c/137?
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c/274
The speed varies as 1/n. If the first-orbit speed is c/137, then for n = 2 it becomes (c/137)/2 = c/274.
The energy of an electron in the ground state of hydrogen is -13.6 eV. What is the total energy of the electron in the fourth orbit?
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-0.85 eV
For hydrogen, En = -13.6/n^2 eV. For n = 4, En = -13.6/16 = -0.85 eV.
A hydrogen atom changes from n = 4 to n = 1. What is the energy of the emitted photon?
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12.75 eV
Energy at n = 4 is -0.85 eV and at n = 1 is -13.6 eV. The emitted photon energy is the difference: -0.85 - (-13.6) = 12.75 eV.
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