Question

7. The isotope cesium-137, which has a half-life of 30 years, is a product of nuclear power plants. How long will it take for this isotope to decay to about one-half of its original amount?
(a) 0 years
(b) 15 years
(c) 30 years
(d) 60 years
@Abhisar @UnkleRhaukus

Answer 1

So with the formula is B?

Answer 2

The half-life of a substance is the time it takes for half of it to decay

Answer 3

\(\huge\frac{1}{2}\) = \(\huge\frac{1}{2^n}\)

Answer 4

n represents the number of times half time has elapsed.

Answer 5

so the answer is 15?

Answer 6

So by solving the above equation u get n= ??

Answer 7

is n 30 or 137?
because if it is 137 then the answer is 68.5

Answer 8

but if n is 30 the answer is 15

Answer 9

n = 1

Answer 10

huh?

Answer 11

1/2^1?

Answer 12

1/2^1 = 1/2

Answer 13

So, n=1

Answer 14

\[\frac{ 1 }{ 2^1 }\]

Answer 15

this means half life has elapsed once

Answer 16

Therefore 30 years have elapsed.

Answer 17

getting my points ?

Answer 18

no

Answer 19

so the answer is C?

Answer 20

so the answer is in the question

Answer 21

i don't get how you get the half life of 30 years

Answer 22

ok wait..brb

Answer 23

brb

Answer 24

The question states the isotope has a half-life of 30 years

Answer 25

The question says that half life of isotope is 30 years

Answer 26

Now, let the number of times half life (30 years) has elapsed be n. Then total time elapsed will be 30n

Answer 27

Formula for finding the fraction of isotope left is \(\huge\frac{1}{2^n}\)

Answer 28

ok

Answer 29

Question says that \(\huge\frac{1}{2}\) is left.

Answer 30

which would make the answer 68.5 or 15 years

Answer 31

This implies that \(\huge\frac{1}{2^n}\)=\(\huge\frac{1}{2}\)

Answer 32

So n=1

Answer 33

Therefore total time elapsed = 30*1=30 years

Answer 34

got it ?

Answer 35

why is in N=1

Answer 36

Solve the equation
\(\color{blue}{\text{Originally Posted by}}\) @Abhisar
This implies that \(\huge\frac{1}{2^n}\)=\(\huge\frac{1}{2}\)
\(\color{blue}{\text{End of Quote}}\)

Answer 37

i don't get why or how N=1

Answer 38

u know how to solve equations ?

Answer 39

ok leave all

Answer 40

Lets do it conceptually

Answer 41

ok

Answer 42

\(\color{blue}{\text{Originally Posted by}}\) @UnkleRhaukus
The half-life of a substance is the time it takes for half of it to decay
\(\color{blue}{\text{End of Quote}}\)

Answer 43

Now the question says that only 1/2 is left i.e half is left and half is decayed

Answer 44

ok