Astronauts on the 1971 Apollo 14 mission to the Moon brought back many rock samples. It is now believed that one of these contains a piece of rock that originated on Earth about 4 billion years (4 × 109 years) ago.
The piece of rock is believed to have been launched into space when an asteroid struck the Earth.
Calculate the number of α particles and the number of β particles emitted for one nucleus of to decay to become a nucleus of .
(2)
Number of α particles = ............................................
Number of β particles = ............................................
The half-lives of the other stages in the decay to are relatively so short that they can be ignored.
There was no lead in the rock when it formed, so all the in the sample is a product of decay. In the sample, for every 103 uranium nuclei present at the start, 50 are now lead nuclei.
Show that the age of the sample is about 4 × 109 years.
(3)
Calculate the minimum speed at which a rock would have to leave the Earth in order to reach the Moon.
In your calculation, you may assume the rock has zero kinetic energy when it has maximum potential energy.
mass of Earth = 5.97 × 1024 kg
radius of Earth = 6370 km
(4)
Minimum speed = ............................................
Calculate the period of the Moon’s orbit four billion years ago, when the radius of its orbit was 1.34 × 108 m.
mass of Earth = 5.97 × 1024 kg
(3)
Period = .........................................
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