# Calculate how much of a 1 gram radium sample will remain after 1000 years? The half life of radium is approximately 1600 years.

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### 3 Answers

First, we have to write the equation of radioactive decay of radium, which is:

A = A0*2^(-t/h)

Now, let's identify the terms of the equation:

A0 = 1 gram

t = 1000 years

h = 1600 (half life)

Once identified, let's substitute them into the equation:

A = 1*2^(-1000/1600)

After simplifying:

A = 1/(2^5/8)

**A = 0.648419777 (approximative value)**

Given the half life of any substance the remaining quantity of any substance remaining after a specified period is given by the following formula:

Qt = i*(0.5)^(t/h)

Where:

Qt = Quantity remaining after time t

Q = Initial quantity

t = Actual time elapsed

h = half life

In the given problem:

Q = 1 gram

t = 1000 years

h = 1600 years

Applying these values to the equation for remaining quantity we get:

Qt = 1*(0.5)^(1000/1600) = 0.5^(1/1.6) = 0.5^0.625

= 0.6484197 = 0.64842 gram (approximately)

Answer:

0.64842 gram of radium sample will remain after 1 year.

Half life of radium is 1600 years.

So for every period of x/1600 years, the (1/2)^(x/1600) of one gram of radium remains.

So after 1000 years (1/2)^(1000/1600) gram remains = 0.648419777 gram out of 1gram radium remains.