Essential University Physics (3rd Edition)
3rd Edition
ISBN: 9780134202709
Author: Richard Wolfson
Publisher: PEARSON
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Question
Chapter 39, Problem 51P
(a)
To determine
The size of a muonic atom.
(b)
To determine
The ground state energy of a muonic atom.
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Although muons have a half-life of 2.2 µs, physical chemists have been able to construct various muonic elements out of them. Replacing the electron with a muon in hydrogen, what is the Bohr radius (in m) of this muonic hydrogen in the ground state? (The mass of a muon is 1.88 ✕ 10−28 kg.)
In solid helium the spacing between atoms is about 3Å . Helium contains 2 protons and 2 neutrons, so the mass of a helium atom is 6.6×10−27 kg. What is the smallest possible energy of a helium atom in solid helium? What temperature (in Kelvin) does this energy correspond with? (Boltzmann's constant is kb=1.38×10−23 J/K
Consider a “muonic atom,” which consists of a proton and a negative muon, symbol -μ. Compute the ground-state energy following the methods used for the hydrogen atom.
Chapter 39 Solutions
Essential University Physics (3rd Edition)
Ch. 39 - Prob. 1FTDCh. 39 - Prob. 2FTDCh. 39 - Prob. 3FTDCh. 39 - Prob. 4FTDCh. 39 - Prob. 5FTDCh. 39 - Prob. 6FTDCh. 39 - Prob. 7FTDCh. 39 - Prob. 8FTDCh. 39 - Name the fundamental force involved in (a) binding...Ch. 39 - Prob. 10FTD
Ch. 39 - Prob. 11FTDCh. 39 - Prob. 12FTDCh. 39 - Prob. 13FTDCh. 39 - Prob. 14FTDCh. 39 - Describe the origin of the cosmic microwave...Ch. 39 - Prob. 16FTDCh. 39 - Prob. 17FTDCh. 39 - The radiation that we observe as the cosmic...Ch. 39 - Prob. 19FTDCh. 39 - Prob. 20FTDCh. 39 - Prob. 21ECh. 39 - Prob. 22ECh. 39 - Prob. 23ECh. 39 - Prob. 24ECh. 39 - Prob. 25ECh. 39 - Prob. 26ECh. 39 - Prob. 27ECh. 39 - Prob. 28ECh. 39 - Prob. 29ECh. 39 - Prob. 30ECh. 39 - Prob. 31ECh. 39 - Prob. 32ECh. 39 - Prob. 33ECh. 39 - Prob. 34ECh. 39 - Prob. 35ECh. 39 - Prob. 36ECh. 39 - Prob. 37ECh. 39 - Prob. 38PCh. 39 - Prob. 39PCh. 39 - Prob. 40PCh. 39 - Prob. 41PCh. 39 - Prob. 42PCh. 39 - Prob. 43PCh. 39 - Prob. 44PCh. 39 - Prob. 45PCh. 39 - Prob. 46PCh. 39 - Prob. 47PCh. 39 - Prob. 48PCh. 39 - Prob. 49PCh. 39 - Prob. 50PCh. 39 - Prob. 51PCh. 39 - Prob. 52PCh. 39 - Prob. 53PCh. 39 - Prob. 54PCh. 39 - Prob. 55PCh. 39 - Prob. 56PCh. 39 - Prob. 57PCh. 39 - Prob. 58PCh. 39 - Prob. 59PCh. 39 - Prob. 60PCh. 39 - Prob. 61PPCh. 39 - Prob. 62PPCh. 39 - Prob. 63PPCh. 39 - Prob. 64PP
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- What is the minimum energy (measured in eV) required to ionize a Hydrogen atom in the level n=r?arrow_forwardA proton captures a µ-[A negative muon is unstable elementary particle] to form a muonic atom of radius (O.285 pm) of the first Bohr orbit of this atom. The mass of the muonic atom [in MeV] is.... * O 94.45 O 944.5 O 93.45 9.44arrow_forwardA hydrogen atom in an excited state can be ionized with less energy than when it is in its ground state. What is n for a hydrogen atom if 0.278 eV of energy can ionize it?arrow_forward
- Doubly ionized lithium (Li++) emits a photon after transitioning from the n = 3 excited state directly back to the ground state. A) Calculate the mass of the lithium ion. (Atomic mass = 6.015123 u; electron mass = 5.485799 x 10-4 u) Express your answer in unified atomic mass units and to four significant figures. B) After the emission of the photon, the ion recoils. Calculate the recoil speed. Express your answer to three significant figures in meters/second.arrow_forwardThe least massive particle known to exist is the electron neutrino. Though scientists once believed that it had no mass, like the photon, they have now determined that this particle has an extremely low mass, equivalent to a few electron volts. Assuming a mass of 2.2 eV/c2 (or 3.9 × 10-36 kg) and a speed of 4.4 × 106 m/s, which of the following values equals the neutrino’s de Broglie wavelength? a. 3.8 × 10-5 m b. 4.7 × 10-7m c. 1.7 × 10-10m d. 8.9 × 10-14marrow_forwardThese values may be useful for the following question(s). speed of light = 3.00 ´ 108 m/s 1 J = 1 kg·m2/s2 1 cal = 4.18 J What is the binding energy of an atom having a mass deficiency of 0.4721 amu per atom? Express your answer in kJ/mol of atoms.arrow_forward
- The muon is unstable and has a mean lifetime of about 2.2 microseconds. A muon is an elementary particle similar to the electron. with an electric charge of -1 e, but with a much greater mass. The mass of a muon is 0.1135u, where the Atomic mass unit u = 1.66 x 10^-27 kg. It decays into an electron and two neutrinos. What is the energy released in this decay (in MeV)? Recall 1 eV = 1.6 x 10^-19 J).arrow_forward(a) How much energy is required to cause an electron in hydrogen to move from the n = 2 state to the n = 3 state?__________ eV(b) If the electrons gain this energy by collision between hydrogen atoms in a high temperature gas, find the minimum temperature of the heated hydrogen gas. The thermal energy of the heated atoms is given by 3kBT/2, where kB is the Boltzmann constant.__________ Karrow_forwardAn alpha particle is made up of two neutrons and two protons in a bound state. Consider a stationary alpha particle a distance d=5.5nm from a neutral hydrogen atom. 1. What is the force between the alpha particle and the hydrogen atom? 2. What is the strength of the force between the alpha particle and the hydrogen atom? 3. The energy needed to ionize the hydrogen atom is U=2.179x10^-18J. What is the closest the hydrogen atom can get to the alpha particle?arrow_forward
- 4. In Section 1.3 we used dimensional analysis to show that the size of a hydrogen atom can be understood by assuming that the electron in the atom is wave-like and non-relativistic. In this problem we show that, if we assume the electron in the atom is a classical electron described by the theory of relativity, dimensional analysis gives an atomic size which is four orders of magnitude too small. Consider a relativistic, classical theory of an electron moving in the Coulomb potential of a proton. Such a theory only involves three physical constants: m, /4mc9, and e, the maximum velocity in relativity. Show that it is possible to construct a length from these three physical constants, but show that it too small to characterize the size of the atom.arrow_forward7)Solve the sub-part (a) only.arrow_forwardA proton is in an infinite box in the n =2 state and its energy is 1.71MeV. How much energy must be added to the proton to put it in a state with n =13 (in MeV)?arrow_forward
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