Question

11 All helium on earth is from the decay of naturally occurring heavy radioactive elements such as uranium. Each alpha particle that is emitted ends up claiming two electrons, which makes it a helium atom. If the original $^{238}U$ atom is in solid rock (as opposed to the earth's molten regions), the He atoms are unable to diffuse out of the rock. This problem involves dating a rock using the known decay properties of uranium 238. Suppose a geologist finds a sample of hardened lava, melts it in a furnace, and finds that it contains 1230 mg of uranium and 2.3 mg of helium. $^{238}U$ decays by alpha emission, with a half-life of $4.5 imes 10^9$ years. The subsequent chain of alpha and electron (beta) decays involves much shorter half- lives, and terminates in the stable nucleus $^{206}Pb$. Almost all natural uranium is $^{238}U$, and the chemical composition of this rock indicates that there were no decay chains involved other than that of $^{238}U$. (a) How many alphas are emitted per decay chain? [Hint: Use conservation of mass.] (b) How many electrons are emitted per decay chain? [Hint: Use conservation of charge.] (c) How long has it been since the lava originally hardened?

          11
All helium on earth is from the decay of naturally occurring
heavy radioactive elements such as uranium. Each alpha particle
that is emitted ends up claiming two electrons, which makes it a
helium atom. If the original $^{238}U$ atom is in solid rock (as opposed
to the earth's molten regions), the He atoms are unable to diffuse
out of the rock. This problem involves dating a rock using the
known decay properties of uranium 238. Suppose a geologist finds
a sample of hardened lava, melts it in a furnace, and finds that it
contains 1230 mg of uranium and 2.3 mg of helium. $^{238}U$ decays by
alpha emission, with a half-life of $4.5 	imes 10^9$ years. The subsequent
chain of alpha and electron (beta) decays involves much shorter half-
lives, and terminates in the stable nucleus $^{206}Pb$. Almost all natural
uranium is $^{238}U$, and the chemical composition of this rock indicates
that there were no decay chains involved other than that of $^{238}U$.
(a) How many alphas are emitted per decay chain? [Hint: Use
conservation of mass.]
(b) How many electrons are emitted per decay chain? [Hint: Use
conservation of charge.]
(c) How long has it been since the lava originally hardened?

11
All helium on earth is from the decay of naturally occurring
heavy radioactive elements such as uranium. Each alpha particle
that is emitted ends up claiming two electrons, which makes it a
helium atom. If the original ^238U atom is in solid rock (as opposed
to the earth's molten regions), the He atoms are unable to diffuse
out of the rock. This problem involves dating a rock using the
known decay properties of uranium 238. Suppose a geologist finds
a sample of hardened lava, melts it in a furnace, and finds that it
contains 1230 mg of uranium and 2.3 mg of helium. ^238U decays by
alpha emission, with a half-life of 4.5 imes 10^9 years. The subsequent
chain of alpha and electron (beta) decays involves much shorter half-
lives, and terminates in the stable nucleus ^206Pb. Almost all natural
uranium is ^238U, and the chemical composition of this rock indicates
that there were no decay chains involved other than that of ^238U.
(a) How many alphas are emitted per decay chain? [Hint: Use
conservation of mass.]
(b) How many electrons are emitted per decay chain? [Hint: Use
conservation of charge.]
(c) How long has it been since the lava originally hardened?

Added by Jose W.

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