Question

Каким было начальное количество радиоактивных атомов, если спустя время t=T/4, где Т-период полураспада, их осталось 5000?

Answer 1

Дано   t=T/4      N=500    No - ?

N=No/2^1/4

No=N*2^1/4

No^2=N^2*2^1/2=5000^2*1,41

N=5000*√1,41=5937 - ответ

Answer 2

N = No/2^t/T 

No = N*2^t/T

No = 5000*2^0.25 

$\sqrt[4]{2} = 2 ^{\frac{1}{4} }$

Answer 3

Initial Amount of Radioactive Atoms and Time

To calculate the initial amount of radioactive atoms, given that after a time t = T/4, where T is the half-life, there are 5000 atoms remaining, we can use the radioactive decay formula.

The general radioactive decay formula is given by:

N(t) = N0 * (1/2)^(t/T)

Where: - N(t) = the quantity of radioactive material at time t - N0 = the initial quantity of radioactive material - t = time that has passed - T = the half-life of the radioactive material

We are given that after a time t = T/4, the quantity of radioactive material remaining is 5000. We can use this information to find the initial quantity of radioactive material, N0.

Calculation

Using the given information, we can set up the equation as follows:

5000 = N0 * (1/2)^(T/4 / T)

Solving for N0:

N0 = 5000 * 2^(1/4)

Result

The initial amount of radioactive atoms, N0, can be calculated using the formula:

N0 = 5000 * 2^(1/4)

By evaluating this expression, we find the initial amount of radioactive atoms.