Respuesta :
Answer: A) 0.0480 grams and B) 56.16 years.
Explanation: Half live is the time in which the amount of radioactive substance remains halve of its initial amount.
The formula we use for solving this type of problem is:
[tex]\frac{N}{N_0}=(\frac{1}{2})^n[/tex]
where, [tex]N_0[/tex] is the initial amount and N is the remaining amount of radioactive substance and n is the number of half lives.
[tex]n=T/t_1_/_2[/tex]
where, T is the time and [tex]t_1_/_2[/tex] is half life.
A) from given data, [tex]N_0[/tex] = 2 g
T = 70 years
[tex]t_1_/_2[/tex] = 13 years
N= ?
[tex]n=\frac{70years}{13years}[/tex]
n = 5.38
[tex]\frac{N}{2g}=(\frac{1}{2})^5^.^3^8[/tex]
[tex]\frac{N}{2g}=0.0240[/tex]
N = 0.0480 g
So, 0.0480 grams of the substance will be remaining after 70 years.
B) [tex]N_0[/tex] = 2 g
N = 0.1 g
T = ?
Let's first calculate the value of n for this.
[tex]\frac{0.1}{2}=(\frac{1}{2})^n[/tex]
[tex]0.05=0.5^n[/tex]
Taking log to both sides:
[tex]log0.05=nlog0.5[/tex]
[tex]-1.301=n(-0.3010)[/tex]
[tex]n=\frac{1.3010}{0.3010}[/tex]
n = 4.32
Half life is 13 years, so we can calculate the time as:
[tex]n=T/t_1_/_2[/tex]
[tex]T=n*t_1_/_2[/tex]
[tex]T=4.32*13years[/tex]
T = 56.16 years
So, it will take 56.16 years for the radioactive substance to decay from 2 g to 0.1 g.
Answer:
Explanation:
a ) 70 years = 70/13 = 5.3846 half years
fraction of matter remaining = (1/2)⁵°³⁸⁴⁶ = 0.02393
g of matter remaining = .02393 x 2 = .0479 g
b ) t = 1/λ ln 2/.1
λ is decay contant and t is time required to convert 2 g to .1 g
λ = .693 / 13 = .0533
t = 1 / .0533 ln 20
= 18.76 x 2.995 = 56.2 years.
