A sample of radium weighs 1000g.How long will it take to decay to 125g if its half-life is 1620 years?
counting half lifes
1000/500/250/125 that is three half lives. or 1620x3 years.
Now, math 1 way/
125=1000((1/2)^halflives
taking logs of each side.
log 125=log 1000+halflives*log(1/2)
(log125-log1000)/log(1/2) = halflives
halflives = (2.07-3)/.301=3.08 halflives (note I rounded log 125)
When one uses halflives,rounding errors often matter.
Yes
To determine how long it will take for the sample of radium to decay to 125g, we can use the half-life formula. The half-life of radium is given as 1620 years.
Let's break down the problem step-by-step:
Step 1: Calculate the number of half-lives required to reach 125g.
The starting mass is 1000g, and the target mass is 125g. Each half-life reduces the mass to half of its previous value. Thus, we need to determine how many times the mass of the radium will halve to reach 125g.
1000g / 2 = 500g (1st half-life)
500g / 2 = 250g (2nd half-life)
250g / 2 = 125g (3rd half-life)
It will take 3 half-lives to reach 125g.
Step 2: Calculate the time required for 3 half-lives.
Since each half-life is given as 1620 years, we need to multiply this value by the number of half-lives (3):
1620 years * 3 = 4860 years
Therefore, it will take 4860 years for the radium sample to decay to 125g.
To determine how long it will take for the sample of radium to decay to 125g, we need to use the concept of radioactive decay and the information given about its half-life.
Here's how you can calculate it step by step:
Step 1: Understand the concept of half-life
The half-life of a radioactive substance is the time it takes for half of the material to decay. In this case, the half-life of radium is given as 1620 years. This means that after every 1620 years, the amount of radium will be halved.
Step 2: Calculate the number of half-lives
To determine the number of half-lives, we need to find the ratio between the initial mass and the final mass. In this case, the initial mass is 1000g and the final mass is 125g. Therefore, the ratio is 125/1000 = 1/8.
Since each half-life reduces the mass by half, we can calculate the number of half-lives by finding the base-2 logarithm of the ratio. Using the formula log(base 2) (1/8), we get -3.
Step 3: Calculate the time
Now that we know the number of half-lives (-3), we can multiply it by the length of each half-life (1620 years) to calculate the total time it will take to reach the final mass.
-3 * 1620 = -4860 years
The negative sign indicates that the decay process is going backward in time. However, since time cannot be negative, we take the absolute value, which gives us 4860 years.
Therefore, it will take approximately 4860 years for the sample of radium to decay to 125g.