Radioactive uranium‐238 decays sequentially into thirteen other lighter elements until it stabilizes at lead‐206. The half‐lives of the fifteen different elements in this decay chain vary from 0.000 164 seconds (from polonium‐214 to lead‐210) all the way up to 4.47 billion years (from uranium‐238 to thorium‐234).

Complete question is;

Lead- 206 is not radioactive, so it does not spontaneously decay into lighter elements. Radioactive elements heavier than lead undergo a series of decays, each time changing from a heavier element into a lighter or more stable one. Eventually, the element decays into lead-206 and the process stops. So, over billions of years, the amount of lead in the universe has increased because of the decay of numerous radioactive elements produced by supernova explosions. Radioactive uranium- 238 decays sequentially into thirteen other lighter elements until it stabilizes at lead- 206. The half-lives of the fifteen different elements in this decay chain vary from 0.000 164 seconds (from polonium- 214 to lead- 210 ) a|| the way up to 4.47 billion years (from uranium- 238 to thorium- 234 ). Find the decay rate per billion years for uranium- 238 to decay into thorium- 234 . Round your answer to one decimal place.

0.14363

Step-by-step explanation:

We are told that time could be all the way up to 4.47 billion years.

Now, formula for half life exponential equation is;

N = N_o•e^(λt)

In this case, N = ½N_o

Thus;

½N_o = N_o•e^(-λt)

N_o will cancel out to give;

½ = e^(-λt)

In ½ = -λt

-0.6931 = -λt

Putting 4.47 for t, we have;

-0.6931 = -4.47λ

λ = 0.6931/4.47

λ = 0.155056

Now, formula for decay rate constant is;

N_t = N_o(e^(-λt))

Since we want to find the decay rate per billion years, then t = 1.

Thus;

Putting 0.155056 for λ and 1 for t, we have;

N_t = N_o(e^(-0.155056 × 1))

N_t = N_o(0.85637)

N_t/N_o = 0.85637

Thus decay rate per 1 billion years is;

1 - 0.85637 = 0.14363

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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step-by-step explanation: