The number of U-238 atoms remaining after 9 billion years will be 12,500.
Half-life is given as the time taken by an object to reduce its concentration to half from the initial.
The half-life can be given as:
[tex]\rm Remaining\;quantity= Initial\;quantity \;\times\;\dfrac{1}{2}^{\frac{t}{t1/2}}[/tex]
The uranium has a half-life 4.5 billion years, the uranium left after 9 billion years from 50,000 atoms will be:
[tex]\rm Remaining\;atoms=50,000\;\times\;\dfrac{1}{2}^{\frac{9}{4.5}}\\\\Remaining\;atoms=50,000\;\times\;0.25\\\\Remaining\;atoms=12,500\;atoms[/tex]
The number of U-238 atoms remaining after 9 billion years will be 12,500.
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