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2 years ago

a sample contains 100 g of radioactive isotope. How much radioactive isotope will remain in the sample after 1 half-life?

Physics

1 answer:

kap26 [50]2 years ago

8 0

Answer:

$\huge\boxed{50g}$

Definition:

Half-life- The time taken for half of the radioactive isotopes to decay.

Explanation:

How does radioactive decay work? Radioactive decay is a process by which unstable nuclei become more stable through the emission of alpha or beta particles or gamma rays.

Since a half-life is the time taken for half of the isotopes to decay, we can simply divide the initial mass of 100 grams by 2; this gives us 50 grams.

1) Divide 100g by 2.

$\frac{100g}{2}=50g$

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We may solve this problem by comparing with the time period of the earth . We know that time period of earth is 365.5 days

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The distance of venus from sun is 0.723 AU i.e $R_{2} =0.723$

From keplers law we know that- $\frac{T_{1} ^{2} }{T_{2} ^{2} } =\frac{R_{1} ^{3} }{R_{2} ^{3} }$

⇒ $T_{2} ^{2} =T_{1} ^{2} *\frac{R_{2} ^{3} }{R_{1} ^{3} }$

Putting the values mentioned above we get-

$T_{2} ^{2} =50,350.132851075$

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