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In Rutherford's famous scattering experi-ments (which led to the planetary model ofthe atom), alpha particles (having charges of+2 e and masses of 6.64 x 10toward a gold nucleus with charge +79 e. Analpha particle, initially very far from the goldnucleus, is fired at 2.37 x 10 m/s directlytoward the gold nucleus.27kg)were fired79e2e+ +How close does the alpha particle getto the gold nucleus before turning around?Assume the gold nucleus remains station-The charge onan electron isary1.602 x 1019 C and the Coulomb constantleis 8.98755 x 109 N- m2/C2Answer in units of m

Question
In Rutherford's famous scattering experi-
ments (which led to the planetary model of
the atom), alpha particles (having charges of
+2 e and masses of 6.64 x 10
toward a gold nucleus with charge +79 e. An
alpha particle, initially very far from the gold
nucleus, is fired at 2.37 x 10 m/s directly
toward the gold nucleus.
27
kg)
were fired
79e
2e
+ +
How close does the alpha particle get
to the gold nucleus before turning around?
Assume the gold nucleus remains station-
The charge on
an electron is
ary
1.602 x 1019 C and the Coulomb constant
le
is 8.98755 x 109 N- m2/C2
Answer in units of m
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In Rutherford's famous scattering experi- ments (which led to the planetary model of the atom), alpha particles (having charges of +2 e and masses of 6.64 x 10 toward a gold nucleus with charge +79 e. An alpha particle, initially very far from the gold nucleus, is fired at 2.37 x 10 m/s directly toward the gold nucleus. 27 kg) were fired 79e 2e + + How close does the alpha particle get to the gold nucleus before turning around? Assume the gold nucleus remains station- The charge on an electron is ary 1.602 x 1019 C and the Coulomb constant le is 8.98755 x 109 N- m2/C2 Answer in units of m

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Step 1

The above problem can be understood as a case of energy conservation.

As the charges on both the alpha particle and the gold nucleus are postive and the gold nucleus being stationary, the alpha particle will eventually begin to slow down as it reaches near the gold nucleus due to repulsion.

Step 2

Initially when the alpha particle is very far from the gold nucleus the repulsive effect on it due to the stationary gold nucleus would be negligible and it can be assumed to possess total energy in the form of kinetic energy.

As the alpha particle begins to approach the gold nucleus, the alpha particle and the gold nucleus will together possess electrical potential energy due to the repulsion between them.

Step 3

Let the kinetic energy of the alpha particle at a very large distance from the nucleus and at the turning point close to the nucleus be denoted as Ki and Kf .

Let the electrical potential energy of the system of a...

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