In an experiment on the transport of nutrients in a plant's root structure, two radioactive nuclides X and Y are used. Initially, 2.70 times more nuclei of type X are present than of type Y. At a time 2.50 d later, there are 4.60 times more nuclei of type X than of type Y. Isotope Y has a half-life of 1.50 d. What is the half-life of isotope X?

Explanation:

From radioactive equation, it is know that,

N = No•exp(-λt)

Where λ is the decay constant

N is is the material remaining after time t

No is the original material at the beginning I.e. at t = 0

Half-life is given as

T½ = In(2) / λ

Now

Given that,

The initial number of nuclides of type X to that of type Y is

No(X) / No(Y) = 2.7

The final number of nuclides of type X to that of type Y is

N(X) / N(Y) = 4.7

The time elapsed between this period is

t = 2.5d

the half life of isotope Y is

T½(Y) = 1.5d

What is the half life of isotope X

From first equation at t = 2.5d

For type X

N = No•exp(-λ•t)

N(X) = No(X) • exp(-2.5•λx)

For Type Y

N = No•exp(-λ•t)

N(Y) = No(Y) • exp(-2.5•λy)

Divide N(X) by N(Y)

Then, we have

N(X) / N(Y) = [No(X) / No(Y)]•exp(-2.5λx) / exp(-2.5λy)

Let substitute the given ratio

4.7 = 2.7 exp(-2.5λx+2.5λy)

4.7 / 2.7 = exp(-2.5λx+2.5λy)

1.741 = exp(-2.5λx+2.5λy)

Take In of both sides

In(1.741) = -2.5λx+2.5λy

0.5543 = -2.5(λx-λy)

(λx-λy) = 0.5543/-2.5

(λx-λy) = -0.2217 equation 1

From the second equation

T½ = In2 / λ

For Type Y

T½(Y) = In2 / λy

λy = In2 / T½(Y)

λy = In2 / 1.5d

λy = 0.4621 /d

From equation 1

λx-λy = -0.2217

λx - 0.4621 = -0.2217

λx = -0.2217 + 0.4621

λx = 02204 /d

Finally,

T½(X) = In2 / λx

T½(X) = In2 / 0.2204 /d

T½(X) = 2.8833 d

So the half life of Element X is 2.8833d

as we know our atmosphere or air have different levels. every level has other gasses, and every gas has another permeability. when the light comes from lower permeability to higher permeability, it changes its direction. so that means that when the light comes from the moon to the earth, it changes it's direction many more times. it basically means that the shape of the light part of the moon is changed on the earth.

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