Radium-226 is a radioactive element, and its decay rate is modeled by the equation r = r0e-0.000428t. how many years will it take for 100 grams of radium-226 to reduce to half its mass? 810 1,620 2,690 5,380

1620 years

Step-by-step explanation:

Given : Radium-226 is a radioactive element, and its decay rate is modeled by the equation R = R0e-0.000428t

Solution:

We will find total number of particles in 100 gram sample :

    Ro = 100 grams * 1 mol / 226 g = 0.4425 mol

Now we will find total number of particles when the 100 gram sample is reduced to half its mass:

    R = Ro/2 = 0.4425/2 = 0.2212

On substituting values of Ro and R to the decay rate equation, we get

    R = Ro e^-0.000428t

     0.2212   = 0.4425 e^-0.000428t

        = e^-0.000428t

Now, take natural logarithm on both sides of the equation in order to find value of t .

    ln (0.2212/0.4425) = -0.000428t

    t= ln (0.2212/0.4425) / (-0.000428)

    t = 1620 years

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1

the 2 figures are congruent bc if you reflect abcd over the y axis then over the d axis the figures overlap