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Modern Physics for Scientists and Engineers [EXP-46432]
176 SOLVED PROBLEMS
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Question: 7.14
(a) Calculate the average orbital radius of a 3d electron in the hydrogen atom. Compare with the Bohr radius for a n = 3 electron. (b) What is the probability of a 3d electron in the hydrogen atom being at a greater radius than the n = 3 Bohr electron? Strategy We used a similar strategy in Example
Verified Answer:
(a) The expectation value of the radial position o...
Question: 10.2
(a) Given that the spacing between vibrational energy levels of the HCl molecule is 0.36 eV, calculate the effective force constant. (b) Find the classical temperature associated with this difference between vibrational energy levels in HCl. Strategy (a) Because κ = μω^2 we first need to find μ and
Verified Answer:
(a) If we assume the most common chlorine-35 isoto...
Question: 14.10
(a) How much energy was available in the center of mass for the experiment of Segrè and Chamberlain, who used 6.4-GeV protons on a fixed proton target to produce antiprotons in the reaction given here? p + p → p + p + p + p (b) How much beam energy was necessary to produce the antiprotons? (c) How
Verified Answer:
(a) If we use Equation (14.10) and the rest energy...
Question: 3.12
(a) What frequency of light is needed to produce electrons of kinetic energy 3.00 eV from illumination of lithium? (b) Find the wavelength of this light and discuss where it is in the electromagnetic spectrum. Strategy We have enough information to determine the photon energy needed from Equation
Verified Answer:
From Equation (3.30), we have
\begin...
Question: 2.13
A 2.00-GeV proton hits another 2.00-GeV proton in a headon collision. (a) Calculate v, β, p, K, and E for each of the initial protons. (b) What happens to the kinetic energy? Strategy (a) By the convention just discussed, a 2.00-GeV proton has a kinetic energy of 2.00 GeV. We use Equation (2.65) to
Verified Answer:
(a) We use K = 2.00 GeV and the proton rest energy...
Question: 12.19
A bone suspected to have originated during the period of the Roman emperors was found in Great Britain. Accelerator techniques gave its ^14C/^12C ratio as 1.10 × 10^-12. Is the bone old enough to have Roman origins? Strategy Remember that the initial ratio of ^14C/^12C at the time of death was
Verified Answer:
The number of
{ }^{14} C \text { atoms deca...
Question: 11.6
A CD stores 700 MB of data. The region of the CD that stores data has an inner radius of 2.30 cm and outer radius of 5.80 cm, and the width of the data track is 1.60 m. What is the surface area allowed for each data bit? What are the approximate dimensions of each bit along the track? Strategy
Verified Answer:
The usable area is
A=\pi\left[(0.058...
Question: 3.4
A furnace has walls of temperature 1600°C. What is the wavelength of maximum intensity emitted when a small door is opened? Strategy We assume the furnace with a small door open is a blackbody so that we can determine λmax from Equation (3.14).
Verified Answer:
We first convert the temperature to kelvin. ...
Question: 2.18
A positively charged sigma particle (symbol Σ^+) produced in a particle physics experiment decays very quickly into a neutron and positively charged pion before either its energy or momentum can be measured. The neutron and pion are observed to move in the same direction as the Σ^+ was originally
Verified Answer:
The rest energies of n and
\pi^{+}
...
Question: 12.9
A radioactive sample of mass 1.0 mg has a half-life of 1.0 h, which means that about 50% of the 1-mg sample will decay in 1.0 h. What fraction decays in 2.0 h?
Verified Answer:
At first thought, we might think that another 0.5-...
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