Chapter 42: Q. 53 (page 1237)

A sample contains radioactive atoms of two types, A and B. Initially there are five times as many A atoms as there are B atoms. Two hours later, the numbers of the two atoms are equal. The half-life of A is $0.50 h r$ . What is the half-life of B?

Short Answer

Expert verified

Half life of B is, $1.189 h r$

Step by step solution

Given information

We are given that,

Time is, $t = 2 h r$

Half life of A is, localid="1650485209128" ${(t_{\frac{1}{2}})}_{A} = 0.50 h r$

And no. of atoms of A is equal to that of B.

Simplify

We know that,

$N_{A} = {(N_{A})}_{0} {(\frac{1}{2})}^{\frac{t}{{(t_{\frac{1}{2}})}_{A}}} = {(N_{A})}_{0} {(\frac{1}{2})}^{\frac{2}{0.5}} = {(N_{A})}_{0} {(\frac{1}{2})}^{4} = \frac{{(N_{A})}_{0}}{16}$

Here, $(N_{A})$ is no. of atoms in A after two hours

And localid="1650367252899" ${(N_{A})}_{0}$ is initial no. of atoms in A

As $N_{A} = N_{B}$

Here, $N_{B}$ is no. of atoms in B

And let initial no. of atoms in B is, ${(N_{B})}_{0}$

And half life of B is, $t_{\frac{1}{2}}$

Therefore,

localid="1650485272574" $\frac{{(N_{A})}_{0}}{16} = {(N_{B})}_{0} \times {(\frac{1}{2})}^{\frac{t}{(t_{\frac{1}{2}})}} \frac{5}{16} = {(\frac{1}{2})}^{\frac{2}{t_{\frac{1}{2}}}} \ln (\frac{5}{16}) = \frac{2}{t_{\frac{1}{2}}} \ln (\frac{1}{2}) t_{\frac{1}{2}} = \frac{\ln (\frac{1}{2})}{\ln (\frac{5}{16})} \times 2 = 0.5948 \times 2 = 1.189 h r$

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A sample contains radioactive atoms of two types, A and B. Initially there are five times as many A atoms as there are B atoms. Two hours later, the numbers of the two atoms are equal. The half-life of A is $0.50 h r$ . What is the half-life of B?

Short Answer

Step by step solution

Given information

Simplify

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A sample contains radioactive atoms of two types, A and B. Initially there are five times as many A atoms as there are B atoms. Two hours later, the numbers of the two atoms are equal. The half-life of A is 0.50hr. What is the half-life of B?

Short Answer

Step by step solution

Given information

Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Physics of Motion

Conservation of Energy and Momentum

Nuclear Physics

Linear Momentum

Oscillations

Radiation

Study anywhere. Anytime. Across all devices.

A sample contains radioactive atoms of two types, A and B. Initially there are five times as many A atoms as there are B atoms. Two hours later, the numbers of the two atoms are equal. The half-life of A is $0.50 h r$ . What is the half-life of B?