Question

The radioactive isotope carbon-14 has a half-life of 5730 years. The decay of carbon is?

Answer 1

i put (ln(.5))/(5730) and it says its wrong....

Answer 2

\[_6^{14}\text C(t)=~_6^{14}\text C_0\cdot2^{{-t}/{5730\text {yr}}}\]

Answer 3

where did the 2 come from?

Answer 4

half life

Answer 5

i thought the equation for half life is 2=(ln(.5))/(-lambda)

Answer 6

i mean t=(ln(.5))/(-lambda)

Answer 7

is this equation right?

Answer 8

\[t_{1/2}=\frac{\ln(2)}{\lambda}=\frac{-\ln(2)}{-\lambda}=\frac{\ln(2^{-1})}{-\lambda}=\frac{\ln(0.5)}{-\lambda}\]

Answer 9

so it is correct.....so that means 5730=(ln(.5))/(-lambda)

Answer 10

i then multiplied the lambda on both sides to get (-lambda)*(ln(.5))=5730

Answer 11

i mean (5730)*(-lambda)

Answer 12

then divided by 5730 and got lamda = (ln(.5))/(5730)

Answer 13

somebody please?

Answer 14

\[t_{1/2}=\frac{\ln(2)}{\lambda}\]

\[{\lambda}=\frac{\ln(2)}{t_{1/2}}\approx\frac{0.693}{5730}=\]
about one in the thousand atoms decay every second

Answer 15

*about one in ten thousand atoms decay every second

Answer 16

so its ln(2) not ln(.5)?

Answer 17

can you help me with something another one please?

Answer 18

i think you just dropped a negative sign somewhere

Answer 19

i can try

Answer 20

the derivative of P=.6P(t) and P(0)=1.....How large is the population after 2 years? and How quickly is the population growing after 2 years?

Answer 21

thx :)

Answer 22

for the first one I put e^1.2.,...but wrong