Question

Problem 4. Suppose that 70% of a radioactive substance is gone after 6.43 years. What is the half life of this substance?

Question 1. What is N(t)/N0 in this problem? (2 points)

a. unknown

b. there isn’t such a thing in this problem

c. .70

d. 6.43 years

e. the half life

Question 2. What is the decay constant in this problem? (3 points)

a. 1.76 years

b. 5.34 years

c. 9.76 years

d. 12.5 years

Question 3. Using the radioactive decay equation to find the half life, what should N(t)/N0 equal? (2 points)

a. the half life

b. the decay constant

c. .50

d. none of the above

Question 4. What is the half life of this substance? (3 points)

a. 3.70 years

b. 2.62 months

c. 5.66 years

d. 11.4 years

Answer 1

Q1. We have the general formula for the half life as

N(t) = No(0.5)^t/t half life .........1

So that here we are asking for N(t)/N0 in this problem and we have given that, 70% of a radioactive substance is gone after 6.43 years

So that Here N(t) = 70/100 × No

Therefore N(t)/N0 = 70/100 = 0.70

Hence option C is correct

Q2.decay constant in this problem is given as,

= ln2/T half

And one more relation for decay constant as

N(t) =No e-t×   .........2

so on plugging the value on equating 2 we will get,

0.7 = e^-6.43×

So that,

= 12.5

Q3. N(t)/N0 = e^-t

Which is not matching with any of the options provided so it will be d option correct here.

Q4. Half life is given as,

Nt =No(0.5)^-t/t half

On plunging values we will get

ln(0.3)= ln(0.5) ^6.43/T half

So that form here T half would be,

T half = 3.701 years

Hence option A is correct here.