Modern Physics For Scientists And Engineers
2nd Edition
ISBN: 9781938787751
Author: Taylor, John R. (john Robert), Zafiratos, Chris D., Dubson, Michael Andrew
Publisher: University Science Books,
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Chapter 5, Problem 5.27P
To determine
(a)
The proof that the maximum kinetic energy of the recoiling atom is approximately
To determine
(b)
The energy and the wavelength of the photon emitted when the muon drops from
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If the energy of the system is of the form E = a|x|" where n = 1,2,3,... and a > 0, show that
( E) = {KBT, where is a constant.
ro
[ (₁) = √₁²
Г
= √√₁²* x² +¹e³dx=(r=
(r− 1)!
As shown in the figure below, a bullet is fired at and passes through a piece of target paper suspended by a massless string. The bullet has a mass m, a speed v before the collision with the target,
and a speed (0.516)v after passing through the target.
(a) Before collision
M
V
m
PHAC
The collision is inelastic and during the collision, the amount of energy lost is equal to fraction [(0.423)KE BC] of the kinetic energy of the bullet before the collision. Determine the mass M of the
target and the speed V of the target the instant after the collision in terms of the mass m of the bullet and speed v of the bullet before the collision. (Express your answers to at least 3 decimals.)
V =
M =
M
(b) After collision
Ernest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that nuclei were very small and dense by scattering helium-4 nuclei (4He) from gold-197 nuclei (19 Au). The energy of
the incoming helium nucleus was 7.35 x 10
-13 j, and the masses of the helium and gold nuclei were 6.68 x 10-27 kg and 3.29 x 10-25
kg, respectively (note that their mass ratio is 4 to 197. Assume that the helium
nucleus travels in the +x-direction before the collision.)
(a) If a helium nucleus scatters to an angle of 112° during an elastic collision with a gold nucleus, calculate the helium nucleus' final speed (in m/s) and the final velocity (magnitude in m/s and direction counterclockwise
from the +x-axis) of the gold nucleus.
120°
He nucleus
Gold nucleus
4He speed
m/s
197Au velocity
m/s
197
Au direction
° counterclockwise from the +x-axis
(b) What is the final kinetic energy (in J) of the helium nucleus?
J
Chapter 5 Solutions
Modern Physics For Scientists And Engineers
Ch. 5 - Prob. 5.1PCh. 5 - Prob. 5.2PCh. 5 - Prob. 5.3PCh. 5 - Prob. 5.4PCh. 5 - Prob. 5.5PCh. 5 - Prob. 5.6PCh. 5 - Prob. 5.7PCh. 5 - Prob. 5.8PCh. 5 - Prob. 5.9PCh. 5 - Prob. 5.10P
Ch. 5 - Prob. 5.11PCh. 5 - Prob. 5.12PCh. 5 - Prob. 5.13PCh. 5 - Prob. 5.14PCh. 5 - Prob. 5.15PCh. 5 - Prob. 5.16PCh. 5 - Prob. 5.17PCh. 5 - Prob. 5.18PCh. 5 - Prob. 5.19PCh. 5 - Prob. 5.20PCh. 5 - Prob. 5.21PCh. 5 - Prob. 5.22PCh. 5 - Prob. 5.23PCh. 5 - Prob. 5.24PCh. 5 - Prob. 5.25PCh. 5 - Prob. 5.26PCh. 5 - Prob. 5.27P
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What is the effective spring constant of the forces holding that atom in the crystal? (c) Sitting on a trampoline, a person with mass m sinks a distance Az below the trampoline's normal level surface. (i) If the person gently bounces on the trampoline (without leaving its surface), what would be the person's period of oscillation T? Check: For Az = 20 cm you should find T 0.90 s. (You should not need the person's mass, but if you think you do, assume and state a value.) (ii) Find T for Az = 45 cm. =arrow_forwardErnest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that nuclei were very small and dense by scattering helium-4 nuclei (4He) from gold-197 nuclei (197Au). The energy of the incoming helium nucleus was 7.12 ✕ 10−13 J, and the masses of the helium and gold nuclei were 6.68 ✕ 10−27 kg and 3.29 ✕ 10−25 kg,respectively (note that their mass ratio is 4 to 197). (Assume that the helium nucleus travels in the +x direction before the collision.) (a)If a helium nucleus scatters to an angle of 119° during an elastic collision with a gold nucleus, calculate the helium nucleus' final speed (in m/s) and the final velocity (magnitude in m/s and direction counterclockwise from the +x-axis) of the gold nucleus. 4He speed_____________ m/s 197Au velocity _____________ m/s 197Au direction____________ ° counterclockwise from the +x-axis (b)What is the final kinetic energy (in J) of the helium nucleus? ______________ Jarrow_forwardErnest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that nuclei were very small and dense by scattering helium-4 nuclei (4He) from gold-197 nuclei (197Au). The energy of the incoming helium nucleus was 7.12 ✕ 10−13 J, and the masses of the helium and gold nuclei were 6.68 ✕ 10−27 kg and 3.29 ✕ 10−25 kg,respectively (note that their mass ratio is 4 to 197). (Assume that the helium nucleus travels in the +x direction before the collision.) (a)If a helium nucleus scatters to an angle of 119° during an elastic collision with a gold nucleus, calculate the helium nucleus' final speed (in m/s) and the final velocity (magnitude in m/s and direction counterclockwise from the +x-axis) of the gold nucleus. 4He speed ______m/s 197Au velocity____ m/s 197 Au direction 330.36 ° counterclockwise from the +x-axis (b)What is the final kinetic energy (in J) of the helium nucleus? ___________ Jarrow_forwardErnest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that nuclei were very small and dense by scattering helium-4 nuclei (4He) from gold-197 nuclei (197Au). The energy of the incoming helium nucleus was 7.52 ✕ 10−13 J, and the masses of the helium and gold nuclei were 6.68 ✕ 10−27 kg and 3.29 ✕ 10−25 kg, respectively (note that their mass ratio is 4 to 197). 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Determine the mass M of the target and the speed V of the target the instant after the collision in terms of the mass m of the bullet and speed v of the bullet before the collision. (Express your answers to at least 3 decimals.) Marrow_forwardErnest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that nuclei were very small and dense by scattering helium-4 nuclei (4He) from gold-197 nuclei (197Au ). The energy of the incoming helium nucleus was 8.00×10−13J, and the masses of the helium and gold nuclei were 6.68×10−27kg and 3.29×10−25kg, respectively (note that their mass ratio is 4 to 197). (a) If a helium nucleus scatters to an angle of 120º during an elastic collision with a gold nucleus, calculate the helium nucleus’s final speed and the final velocity (magnitude and direction) of the gold nucleus. (b) What is the final kinetic energy of the helium nucleus?arrow_forwardIn a nuclear scattering experiment, a beam of 4-MeV alpha particles (helium nuclei) strikes a target consisting of helium gas, so that the falling particle and the target particle have equal masses. If the incident alpha particle is dispersed at an angle of in 30° the laboratory system, find its kinetic energy and the kinetic energy of the target particle's recoil, as part of the initial kinetic energy of the incident alpha particle. (Assume the target particle is at rest .and the collision is elastic P2 in which o = 30° +9 = 90° pi p, =0 P = Pi cos , + p2 sin o 0 = p{ sino - p2 cos Pi = P1 cos =p, cos 30° =- 2 P2 = P1 sing = P; sin 30° =. 12 Pi T = 2m, 1 Pi T=1 MeV 2m, Pi -=T= 3 MeV 2m, T = 2m2 %3D 4. Laboratory system H.W. What is the scattering angle with respect to the center of mass system of the previous example (in a nuclear scattering experiment, a beam of alpha-4-MeV particles hits ...)? 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