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Physics 12 Assignment KEY
Chapter 19 – Quantum Theory & the Atom
1. Define the following terms:
• continuous spectrum - a spectrum of light over a range of wavelengths without any spectral lines
• line spectrum - a set of dark or bright lines in an otherwise uniform and continuous spectrum,
resulting from a deficiency or excess of photons in a narrow frequency range, compared with the
nearby frequencies
• emission spectrum - a spectrum that contains bright emission lines
• absorption spectrum - a spectrum that contains dark lines at wavelengths corresponding to normally
emitted lines
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Lyman series - a series of UV spectral lines in the spectrum of hydrogen caused by an electron transitions
Balmer series - a series of visible spectral lines in the spectrum of hydrogen caused by an electron
transitions
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Paschen series - a series of IR spectral lines in the spectrum of hydrogen caused by an electron transitions
quantum number - an integer that describes the orbital or energy level of an electron in an atom
Bohr radius – the distance from the nucleus of the lowest allowed energy level in the hydrogen
atom
ground state – the lowest possible energy state that an electron can occupy in an atom
excited states - states of an atom, ion, or molecule with a higher energy than the ground state
binding energy (or ionization energy) - radiation of sufficient energy to liberate the bound electrons
from the atoms or molecules
2. In Rutherford’s planetary model of the atom, what keeps the electrons from flying off into space?
In Rutherford’s planetary model of the atom, the Coulomb (or electrostatic) force keeps the electrons
from flying off into space. Since the protons in the center are positively charged, the negatively charged
electrons are attracted to the center by the Coulomb force and orbit around the center just like the
planets orbiting the Sun in the Solar System due to attractive gravitational force.
3. How can the spectrum of hydrogen contain so many lines when hydrogen contains only one electron?
Even though hydrogen only has one electron, it still has an infinite number of energy states for that one
electron to occupy and each line in the spectrum represents a transition between two of those possible
energy levels.
4. Use conservation of momentum to explain why photons emitted by hydrogen atoms have slightly less energy
than predicted by the equation Ef – Ei = hf.
When a photon is emitted by a hydrogen atom as the electron makes a transition from one energy state to a lower
one, not only does the photon carry away energy and momentum, but to conserve momentum, the electron must
also take away some momentum. If the electron carries away some momentum, then it must also carry away some
of the available energy, which means that the photon takes away less energy than Ef – Ei = hf predicts.
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Is the transition an absorption or an emission?
Which is higher, the initial state energy of the final state energy of the atom?
Finally, which of these transitions involves the largest energy photon?
(a) n = 1, n’ = 3 (b) n = 6, n’ = 2 (c) n = 4, n’ = 5.
6. What wavelength photon would be required to ionize a hydrogen atom in the ground state and give the
ejected electron a kinetic energy of 10.0 eV?
The energy of the photon is
hf = Eion + Ek =
13.6 eV
+ 10 eV = 23.6 eV
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We find the wavelength from
E photon = hf = 23.6 eV = 3.78072 x 10−18 J
3.78072 x 10−18 J
= 5.705885904 x 1015 Hz
h
6.626 × 10−34 Jis
c
3.00 x 108 m/s
λ= =
= 5.26 x 10−8 m = 52.6 nm
f 5.705885904 x 1015 Hz
∴f =
E photon
=