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The half-life of radium is 1620 years. If a laboratory has 12 grams of radium, how long will it take before it has 8 grams of radium left?
a 947.6 years

b 804.3 years

c 797.5 years

d 849.5 years

Sagot :

Trancescient

Step-by-step explanation:

A = A02^(-t/hl) ---> ln(A/A0) = -(t/hl)ln2

solving for t,

t = -(hl)ln(A/A0)/ln2

= -(1620 yrs)×ln(8/12)/ln2

= 947.6 yrs

974.6 years It will take before it has 8 grams of radium left,

Given that,

The half-life of radium is 1620 years

Laboratory has 12 grams of radium,

We have to determine,

How long will it take before it has 8 grams of radium left.

According to the question,

Laboratory has radium = 12 grams

Left radium = 8 grams

Half life of radium [tex]_t_\frac{1}{2}[/tex] = 1620 years.

[tex]N = N_o [\frac{1}{2}]^{n} \\\\8 = 12 [\frac{1}{2}] ^{n}\\\\\frac{8}{12} } =[ \frac{1}{2} ]^{n}\\\\ log2 - log3 = n( log1 - log2)\\\\0.30-0.47 = n (0 - 0.30)\\\\-0.17 = -0.30 n\\\\n = 0.56[/tex]

It will take before it has 8 grams of radium left,

[tex]t = n \times t_\frac{1}{2} \\\\t = 0.56 \times 1620\\\\t = 974.6 \ years[/tex]

Hence, 974.6 years It will take before it has 8 grams of radium left,

For more information about Half life click the link given below.

https://brainly.com/question/24710827

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