Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
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Chapter 4, Problem 72CE
(a)
To determine
Uncertainty in the energy of emitted photon
(b)
To determine
The range of wavelength
(c)
To determine
Relationship between the
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When a hydrogen atom undergoes a transition from n=3 to n=2 level, a photon with λ=656.5 nm is emitted. (a) If we imagine the atom as an electron in a one-dimensional box, what is the width of the box so that the transition from n=3 to n=2 corresponds to the emission of a photon of this wavelength? (b) For a box with the width calculated in (a), what is the ground energy state? (c) Do you think a one-dimensional box is a good model for a hydrogen atom? Because?
(Hand by writing ans.)A certain atom has an energy level of 3.50 eV above the ground state. When excited to this state, it remains 4.0µs, on average, before emitting a photon and returning to the ground state.
i) What is the energy of the photon? What is the wavelength of the photon?
ii) What is the smallest possible uncertainty in the energy of the photon?
An atom of iron has a radius of
156. pm
and the average orbital speed of the electrons in it is about
×5.7*10^7 m/s.
Calculate the least possible uncertainty in a measurement of the speed of an electron in an atom of iron. Write your answer as a percentage of the average speed, and round it to 2 significant digits.
Chapter 4 Solutions
Modern Physics
Ch. 4 - Prob. 1CQCh. 4 - Prob. 2CQCh. 4 - Prob. 3CQCh. 4 - Prob. 4CQCh. 4 - Prob. 5CQCh. 4 - Prob. 6CQCh. 4 - Prob. 7CQCh. 4 - Prob. 8CQCh. 4 - Prob. 9CQCh. 4 - Prob. 10CQ
Ch. 4 - Prob. 11ECh. 4 - Analyzing crystal diffraction is intimately tied...Ch. 4 - The setup depicted in Figure 4.6 is used in a...Ch. 4 - Prob. 14ECh. 4 - Prob. 15ECh. 4 - Prob. 16ECh. 4 - Prob. 17ECh. 4 - Prob. 18ECh. 4 - Prob. 19ECh. 4 - Prob. 20ECh. 4 - Prob. 21ECh. 4 - Prob. 22ECh. 4 - Prob. 23ECh. 4 - Prob. 24ECh. 4 - Prob. 25ECh. 4 - Prob. 26ECh. 4 - Prob. 27ECh. 4 - Prob. 28ECh. 4 - Prob. 29ECh. 4 - Prob. 30ECh. 4 - Prob. 31ECh. 4 - Prob. 32ECh. 4 - Prob. 33ECh. 4 - Prob. 34ECh. 4 - Prob. 35ECh. 4 - Prob. 36ECh. 4 - Prob. 37ECh. 4 - (a) Experiment X is carried out nine times...Ch. 4 - Prob. 39ECh. 4 - Prob. 40ECh. 4 - Prob. 41ECh. 4 - Prob. 42ECh. 4 - Prob. 43ECh. 4 - Prob. 44ECh. 4 - Prob. 45ECh. 4 - Prob. 46ECh. 4 - Prob. 47ECh. 4 - Prob. 48ECh. 4 - Prob. 49ECh. 4 - Prob. 50ECh. 4 - Prob. 51ECh. 4 - Prob. 52ECh. 4 - Prob. 53ECh. 4 - Prob. 54ECh. 4 - Prob. 55ECh. 4 - Prob. 56ECh. 4 - Prob. 57ECh. 4 - Prob. 59ECh. 4 - Prob. 60ECh. 4 - Prob. 61ECh. 4 - Prob. 62ECh. 4 - Prob. 63ECh. 4 - Prob. 64ECh. 4 - Prob. 65ECh. 4 - Prob. 67ECh. 4 - Prob. 68ECh. 4 - Prob. 71CECh. 4 - Prob. 72CECh. 4 - Prob. 73CE
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- An atom is in an excited state for 4.00 us before moving back to the ground state. Find the approximate uncertainty in energy of the photon in units of 10¹¹ eV. (A) 8.23 (B) 3.78 (C) 4.97 (D) 5.49 (E) 6.17arrow_forward(a) Calculate the speed of an electron that is in the n = 1 orbit of a hydrogen atom, and give your answerv as a fraction of the speed of light in empty space c, for example, v = 0.5 if the answer werev = c/2 = 1.50 × 108 m/s. (It isn’t.)(b) How many nanometers would be the wavelength of the photon emitted when the electron in a hydrogenatom jumps from the n = 3 orbit to the n = 2 orbit? This is the Hα line, and its light is scarlet, the color offresh human blood.(c) How many nanometers would be the wavelength of the photon emitted when the electron in a hydrogenatom jumps from the n = 2 orbit to the n = 1 orbit?(d) How many nanometers would be the wavelength of a photon that would have the minimum amount ofenergy needed to ionize any hydrogen atom? (Hint: Electromagnetic radiation with this wavelength or shorteris called extreme ultraviolet radiation.(e) How many electron-volts (eV) would the electron in part (7)(d) need to have?arrow_forwardSuppose a laser pulse has an average duration of 5.00 femtoseconds and an average energy of 1.81 eV, and it has an uncertainty of 13.8%. What is the highest energy you can observe for a photon in the pulse? (in eV)arrow_forward
- Express the complex number z1 = (√(3) + i)/2 in the form rei Φ. What about z2 = (1 + √(3i))/2? If these complex numbers are the probability amplitudes for photons to be detected, what is the probability in each case? (Hint: See attatched image for more on finding probability amplitudes)arrow_forwardCalculate the electric dipole moment for the transition from the first excited stateY(10) to the ground stateY(20) 2:11 1 m₁ Yim, (0,0) 0 0 ztr 1 0 √cose 1 ±1 2 0 2 ±1 2 +2 Planck's constant = F-1/2 (sin)eti +√√(3 cos² 0-1) F/1/1₁ (cosesin)eti √(sin² (sin² 0)* 1216 e 2:15 -23 m n².kg.S¹².K = 6.6x10-34 Joule-sec Speed of light = 2.9×108 m/sec u = 1.66×10-27 Kg k=1.3806 x10 2:16 ✔arrow_forwardUsing partial derivatives, calculate the propagated uncertainty in the mass in the following case: given the centripetal force Fc = (20.0 ± 0.5) N, the angular velocity w = (29.2 ± 0.3) rad/s, and the radius R = (0.12 ± 0.01) m get the mass value,m = Fc / (w2R). Express the result in the form m = m + Δm ANSWER IS 0.20 +- 0.03 KGAS SAID, USE UNCERTAINTY PROPAGATION SHOWN IN THE IMAGEarrow_forward
- Imagine another universe in which the value of Planck’s constant is 0.0663 J . s, but in which the physical laws and all other physical constants are the same as in our universe. In this universe, two physics students are playing catch. They are 12 m apart, and one throws a 0.25 kg ball directly toward the other with a speed of 6.0 m/s. (a) What is the uncertainty in the ball’s horizontal momentum, in a direction perpendicular to that in which it is being thrown, if the student throwing the ball knows that it is located within a cube with volume 125 cm3 at the time she throws it? (b) By what horizontal distance could the ball miss the second student?arrow_forwardA certain atom remains in an excited state for about 51.7 ns before emitting a 2.15-eV photon and transitioning to the ground state. What is the uncertainty in the frequency of the photon in Hz?arrow_forwardUsing partial derivatives, calculate the propagated uncertainty in the mass in the following case: given the centripetal force Fc = (20.0 ± 0.5) N, the angular velocity w = (29.2 ± 0.3) rad/s, and the radius R = (0.12 ± 0.01) m get the mass value,m = Fc / (w2R). Express the result in the form m = m + Δm ----------------------------------- THAT'S THE QUESTION ASKED, see the image for the answer. Also have a look at the second image, the blue one. --------------------------------------------------------------- Explain what is the 1/m just after the equals sign at the second line of the answer. Also, explain why the answer does not use the square root just like the blue image, of if it is using it. Then, say in which case should I use the partial derivate to calculate the uncertainty.arrow_forward
- A) By what factor is the uncertainty of the electron's position(1.36×10-4 m) larger than the diameter of the hydrogen atom?(Assume the diameter of the hydrogen atom is 1.00×10-8 cm.) B) Use the Heisenberg uncertainty principle to calculate Δx for a ball (mass = 122 g, diameter = 8.50 cm) with Δv = 0.425 m/s. C) The uncertainty of the (above) ball's position is equal to what factor times the diameter of the ball?arrow_forwardConsider an oxygen (O2) molecule in a bottle of air. Imagine that at a certain time, we locate the molecule along the x axis to within an uncertainty of 0.1 nanometers. a) What is the minimum uncertainty in the molecule's x-velocity required by the Heisenberg Uncertainty Principle? (Hint: the answer is about 10 m/s) b) How does this compare (roughly) to the magnitude of the molecule's average x-velocity due to its thermal motion at room temperature? (Hint: the answer is delta v << average thermal speed) (Hint: Avogadro's number of oxygen molecules has a mass of about 32 grams. At an absolute temperature T, a molecule has an average kinetic energy of 1.5 * kB * T, where kB is Boltzmann's constant. Room temperature is about 295 K).arrow_forward(a)What are the energies of the first three energy levels of an electron confined in a one-dimensional box of wavelength 0.70nm. Give your answer in electron volts (eV) (b) How much energy must the electron lose to move from the n=2 energy level to the n=1 energy level? Again, give your answer in eV. (c) Suppose that an electron can move from the n=2 level to n=1 level by emitting a photon of light. If energy is conserved, what must the photon wavelength be? Give your answer in nanometersarrow_forward
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