# Radium-221 has a half-life of 30 seconds. How long will it take for 94% of a sample to decay?

##### 1 Answer

#### Explanation:

Now, the equation for radiation of a radioactive substance is given by the equation

where

Now, apparently for the entire radioactive mass of Radium-221 taken to degrade such that only half of the original mass remains, 30 seconds pass by.

So,

Applying ln (log base e) to both sides of the equation, I get

So that means

So the equation in total is

Now, we're trying to find out how many seconds pass by until

Substituting that into the equation leads us to

Apply ln on both sides give us

You better get your calculator out here, it's turning out to be a tad windy.

Now, the rest is up to you, solve this and save the human race from nuclear annihilation!