Question

I need some help on this difficult assignment, it is biology but can also be considered as math because of the calculation questions

Answer 1

The half life of a radioactive substance tells you how long it takes for half of the original sample to disappear.

What is the half life of C-14?
After one half life, you expect just half as much as what you had initially.

Answer 2

To calculate the amount (A) left after n amount of half lives, we can say

\[A(n) = A_0 \times 0.5^n \] where A0 is the original amount.

Answer 3

This should be rather intuitive. After two half lives we have half of half of the original which is a quarter of the original (50% x 50% = 25%). After three half lives we have 50% x 50% x 50% = 12.5% of the original)

Repeating this pattern, after n half lives we have (50%)^n or 0.5^n of the original sample which the formula above represents.

Answer 4

So is this for part 1?

Answer 5

no part 1 is comprehension for you to consider. Part 2 and 3 are covered

Answer 6

So try and figure them out and see what you come up with.

Answer 7

So for part b wouldn't I just do 6,000*1,000

Answer 8

no that wouldn't make sense would it?
6000 x 1000 is going to give you a BIGGER number. If something undergoes radioactive decay you lose stuff, it gets smaller.

Answer 9

What I recommend you do is focus on what the meaning of half life is for a radioactive substance. Remember I told you the half life is the amount of TIME it takes for exactly HALF of the original sample to decay.

What does it say the half life of C-14 is in your question?

Answer 10

About 6,000 years

Answer 11

ok what is the amount of time that has elapsed in part b?

Answer 12

6,000 years?

Answer 13

ok which is exactly one half life as they have given you. So how much carbon-14 do you expect leftover compared to the original before decay?

Answer 14

0

Answer 15

cause 6,000 is the half life right, and they are saying that 6,000 years have elapsed

Answer 16

0 is not correct but your statement about 6000 years being one half life is correct.
(In fact you can never get 0 for amount). A half life is the time taken for HALF of the stuff to disappear

Answer 17

so after 6000 years (1 half life) you expect to see half of what you had at the beginning.
How much did you start with?

Answer 18

oh okay 3,000 then

Answer 19

Cause half right

Answer 20

Im sorry, Im really struggling with this assignment :/

Answer 21

be careful, you are mixing time and the amount of substance.

When 6000 years (time) has passed, this halves the amount of C-14 you have.
You had 1000 atoms of C-14 to start with.
So after 6000 yrs, you have half of the AMOUNT.
So 1000 x 1/2 = 500 atoms.

Answer 22

So 500?

Answer 23

Do we continue or is this the final answer

Answer 24

well this is the final answer if the time passed in 6000 years.
I hope you're getting the relationship between half life and amount.
Every half life, we halve the amount. That's all.

Answer 25

You can generalise this result to any amount.

If your half life was the same as before (6000 years) and you started with

(i) 10000 atoms of C-14, then after 6000 years, you have 5000 atoms
(ii) 300 atoms of C-14, " " you have 150 atoms
(iii) 5000 atoms of C-14, " ", you have 2500 atoms
(iv) 3kg of C-14, " " you have 1.5 kg of C-14.

Point is after 1 half life, you have half of what you started with.

Answer 26

Part C is a bit more complicated. The time elapsed is not simply 1 half life, so you need to do a bit more work.

First, you need to convert the time elapsed into multiples of half lives.
18000 years is the same as 18000/6000 = 3 half lives.
So this means 3 half lives have passed. Each half life we have half of the original.
So we need to half the original 3 times for 3 half lives.

This is \[1000 \times \frac{ 1 }{ 2 } \times \frac{ 1 }{ 2 } \times \frac{ 1 }{ 2 }\]

In general if you have n half lives you multiply the original amount by 1/2 n times.

Answer 27

so just 1000 * 1/2 * 1/2 * 1/2

Answer 28

?

Answer 29

Here's a helpful table. See if you can fill in the row for 18000 years.