A mine worker discovers an ore sample containing 500 mg of radioactive material. It is discovered that the radioactive material has a half life of 1 day. Find the amount of radioactive material in the sample at the beginning of the 7th day.

Answer:

7.8125 or 7.8

Step-by-step explanation:

[tex]gm=(1/2)^{n-1}[/tex]

[tex]gm=500 (1/2)^{ 7- 1} \\gm= 500 (1/2)^{6}[/tex]

= 7.8125 or 7.8

The amount of radioactive material in the sample at the beginning of the 7th day is 3.906 milligram.

Half life of an element is the time taken by a radioactive substance to break down into half the quantity of the initial quantity.

In other words, we can say that it is the time for an element to disintegrate half of it's atoms.

Given that,

Half life of radioactive material is 1 day.

Initial amount of the substance = 500 mg

At the beginning of the first day, there will be 500 / 2 = 250 mg os substance.

Taking the first term as 250 and the common ratio as 1/2, we can consider this as a geometric sequence.

nth term of a geometric sequence = a rⁿ⁻¹, where a is the first term and r is the common ratio.

At the beginning of seventh day,

Amount of radio active substance = 250 (1/2)⁷⁻¹ = 3.90625

Hence the amount at the beginning of seventh day is 3.906.

Learn more about Geometric Sequence here :

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