3. a) Alpha particles of the same initial speed are shot at the same intensity toward gold, silver, and aluminum foils of the same thickness. They are observed at a detector at a fixed scattering angle, 0 0°. What would the ratios of the number of alpha particles scattered by the gold and silver foils to the aluminum foil, Au NaAl NaAg NaAl and respectively, be? (ZAu = 79, ZAg = 47, ZAI 13). b) Compare the number of a particles of fixed kinetic energy scattered through an angle of 10° (call this No(10°)) with the number scattered through an angle of 20° (Na (20°)) for Rutherford scattering by a thin gold foil of fixed thickness. Compute No (10⁰) Na (20°)* = Rutherford's scattering model assumes that the alpha particles experience a Coulomb repulsion, F = Kaze from the nucleus of the foil's atom. If, in a head-on collision the alpha particle has enough energy to get inside a uniformly charged Kqa Zer nucleus of radius R, the force law would change to F and Rutherford's R³ " point-nucleus calculation would fail. c) Write an expression for the initial kinetic energy of the alpha particle when it is far from the nucleus in the foil in terms of its mass, ma, and its speed, Va.
3. a) Alpha particles of the same initial speed are shot at the same intensity toward gold, silver, and aluminum foils of the same thickness. They are observed at a detector at a fixed scattering angle, 0 0°. What would the ratios of the number of alpha particles scattered by the gold and silver foils to the aluminum foil, Au NaAl NaAg NaAl and respectively, be? (ZAu = 79, ZAg = 47, ZAI 13). b) Compare the number of a particles of fixed kinetic energy scattered through an angle of 10° (call this No(10°)) with the number scattered through an angle of 20° (Na (20°)) for Rutherford scattering by a thin gold foil of fixed thickness. Compute No (10⁰) Na (20°)* = Rutherford's scattering model assumes that the alpha particles experience a Coulomb repulsion, F = Kaze from the nucleus of the foil's atom. If, in a head-on collision the alpha particle has enough energy to get inside a uniformly charged Kqa Zer nucleus of radius R, the force law would change to F and Rutherford's R³ " point-nucleus calculation would fail. c) Write an expression for the initial kinetic energy of the alpha particle when it is far from the nucleus in the foil in terms of its mass, ma, and its speed, Va.
Related questions
Question
Transcribed Image Text:3. a) Alpha particles of the same initial speed are shot at the same intensity
toward gold, silver, and aluminum foils of the same thickness. They are observed at
a detector at a fixed scattering angle, 0 0°. What would the ratios of the number
of alpha particles scattered by the gold and silver foils to the aluminum foil, No Au
13).
NaAl
and respectively, be? (ZAu = 79, ZAg = 47, ZAI
Na Ag
NaAl
b) Compare the number of a particles of fixed kinetic energy scattered through an
angle of 10° (call this Na(10°)) with the number scattered through an angle of 20°
(Na (20°)) for Rutherford scattering by a thin gold foil of fixed thickness. Compute
Na (10⁰)
Na (20°).
p2
Rutherford's scattering model assumes that the alpha particles experience a
Coulomb repulsion, F = KqZe from the nucleus of the foil's atom. If, in a head-on
collision the alpha particle has enough energy to get inside a uniformly charged
Kqa Zer
nucleus of radius R, the force law would change to F =
R³ "
point-nucleus calculation would fail.
and Rutherford's
c) Write an expression for the initial kinetic energy of the alpha particle when it
is far from the nucleus in the foil in terms of its mass, ma, and its speed, Va.
d) Write an expression for the potential energy of the alpha particle during a
head-on collision at its position of closest approach, a distance re from the centre of
the nucleus in terms of K, qa, Z and e.
e) For alpha particles of kinetic energy 1.23×10-¹2 J that were available to Ruther-
ford, calculate the distance of closest approach for the atoms of Ag and Al, assuming
this point-like behaviour continued to these radii and using your results from c) and
d). (Rutherford used deviations of the observed scattering off aluminum foils to es-
timate the radius of the nucleus of the aluminum atom, but did not have sufficiently
high energy alpha particles to estimate the radius of the gold atom as nuclear radii
do not vary quickly with Z.)
2
Expert Solution
Note :
Hi! Thank you for your question. As per the guideline, we can solve three subparts at a time in case of multiple parts. As you have not mentioned for which one you need the answer, we are solving the first three. Please repost the question to get the answers to the rest of the questions.
Step by step
Solved in 5 steps
