WILL GIVE BRAINEST If a radioactive sample starts with 100 g, how many grams of the original substance will be left after 5 half lives? Show your work in the space provided 20 g

50 g

3.125 g

12.5 g

Explanation:Nuclear half-life expresses the time required for half of a sample to undergo radioactive decay. Exponential decay can be expressed mathematically like this:

A

(

t

)

=

A

0

⋅

(

1

2

)

t

t

1/2

(1), where

A

(

t

)

- the amount left after t years;

A

0

- the initial quantity of the substance that will undergo decay;

t

1/2

- the half-life of the decaying quantity.

So, if a problem asks you to calculate an element's half-life, it must provide information about the initial mass, the quantity left after radioactive decay, and the time it took that sample to reach its post-decay value.

Let's say you have a radioactive isotope that undergoes radioactive decay. It started from a mass of 67.0 g and it took 98 years for it to reach 0.01 g. Here's how you would determine its half-life:

Starting from (1), we know that

0.01

=

67.0

⋅

(

1

2

)

98.0

t

1/2

→

0.01

67.0

=

0.000149

=

(

1

2

)

98.0

t

1/2

98.0

t

1/2

=

log

0.5

(

0.000149

)

=

12.7

Therefore, its half-life is  

t

1/2

=

98.0

12.7

=

7.72

years

.

So, the initial mass gets halved every 7.72 years.

Sometimes, if the numbers allow it, you can work backwards to determine an element's half-life. Let's say you started with 100 g and ended up with 25 g after 1,000 years.

In this case, since 25 represents 1/4th of 100, two hal-life cycles must have passed in 1,000 years, since

100.0

2

=

50.0

g

after the first  

t

1/2

,

50.0

2

=

25.0

g

after another  

t

1/2

.

So,  

2

⋅

t

1/2

=

1000

→

t

1/2

=

1000

2

=

500

years

.

Stefan V. ·  5 · Dec 30 2014

What is the half life equation?

T=th xlog(m./m)/log(2)

Explanation:

You could use this formula:

Where Th = half-life.

M. = the beginning amount

M = the ending amount

One example of how to use the equation:

One of the Nuclides in spent nuclear fuel is U-234, an alpha emitter with a half-life of 2.44 x10^5 years. If a spent fuel assembly contains 5.60 kg of U-234, how long would it take for the amount of U-234 to decay to 0.35? First, break down the complicated equation:

T= unknown

Th= 2.44 x10^5 or 244000

M.= 5.60

m= 0.35

Then plug the number into the equation:

T= 244000 xlog(5.60/0.35)/log(2)

T= 244000x1.20412/log(2)

So the Answer is: T= 9.76x10^5 min.

Note: The example was a question from my quiz

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