Physics 2D Quiz #3
Department of Physics, UCSD
Summer Session II - 2009
Prof. Pathria
21 August 2009
Some Useful Data
Speed of light:
c = 2.998×108 m/s.
Planck’s constant:
h = 6.626×10−34 J·s
Coulomb constant:
k = 8.99×109 Nm2 /C 2
Rydberg constant:
R = 1.097 × 107 m−1
Electron charge:
e = 1.602×10−19 C
1 eV = 1.602×10−19 J
Electron rest mass:
me = 9.11×10−31 kg
Electron rest mass energy:
me c2 = 0.511 MeV
Energy of H atom in ground state:
E1 = −13.6 eV
Bohr radius:
a0 = 0.0529 nm
de Broglie wavelength:
λ = h/p
p
√
p = 1c E 2 − (m0 c2 )2 = 1c 2m0 c2 K + K 2
Uncertainty relations:
∆x∆p ≥ h/4π
∆E∆t ≥ h/4π
Instructions
Please write your answers in your blue book, and make sure your secret code
number is written on all pages in indelible ink.
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1. A hydrogen atom happens to be in a state in which its total energy E (kinetic
plus potential) is -3.4 eV.
(a) Using this information, or otherwise, determine the kinetic energy K and
the potential energy U of the system.
(b) Using the value of K found above, determine the wavelength λ of the
electron.
(c) Next, using the value of U , determine the radius r of the electron’s orbit.
(d) What do you think should be the relationship between r and λ in the given
state of the atom? Check if your values of r and λ satisfy this relationship.
2. Calculate the frequency f of the photon emitted by a hydrogen atom making
a transition from the state n = 4 to the state n = 3. Compare your result with
the frequency of revolution f ∗ of the electron in these two orbits.
3. Through what potential difference would an electron have to be accelerated
so that it has a de Broglie wavelength of:
(i) 0.18 nm?
(ii) 0.0018 nm?
4. Consider a photon and an electron that have a common wavelength λ, while
the energy Eγ of the photon is one-half of the total energy Ee of the electron.
(a) What is the value of λ in nm?
(b) What are the values of Eγ and Ee in Mev?
(c) What is the speed of the electron in m/s?
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