Chapter 41: Q. 47 (page 1208)

a. Find an expression in terms of $t$ for the half-life t1/2 of a sample of excited atoms. The half-life is the time at which half of the excited atoms have undergone a quantum jump and emitted a photon. b. What is the half-life of the $3 p$ state of sodium?

Short Answer

Expert verified

a) The expression in terms of $t$ for the half-life $t_{1 / 2}$ of a sample of excited atoms is $0.693 τ$

b) The half-life of the $3 p$ state of sodium is $11.781 n s$

Step by step solution

Part(a) Step 1: Given information

We are given that The half-life is the time at which half of the excited atoms have undergone a quantum jump and emitted a photon .

We need to find expression in terms of $t$ for the half-life $t_{1 / 2}$ of a sample of excited atoms ,

Part(a) Step 2: Simplify

We will use exponential decay law which is , $N_{e} (t_{1 / 2}) = \frac{1}{2} N_{0}$ where $t_{1 / 2}$ is half life .Let this be equation $1$ .

We will write this as $N_{e} (t_{1 / 2}) = N_{0} e^{- \frac{t_{1 / 2}}{τ}}$ .

Comparing both the equation and taking logarithm on both the sides

, role="math" localid="1650441078255" $e^{\frac{- t_{1 / 2}}{τ}} = \frac{1}{2} t_{1 / 2} = τ \ln 2$

Substituting , $t_{1 / 2} = 0.693 τ$

Part(b) Step 1: Given information

We need to find out half-life of the $3 p$ state of sodium.

Part(b) Step 2: Simplify

We need to find half life , We will use this equation for half life , $t_{1 / 2} = \ln 2 τ$

Simplifying , we get $t_{1 / 2} = (0.693) (17 n s) = 11.781 n s$ .

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a. Find an expression in terms of $t$ for the half-life t1/2 of a sample of excited atoms. The half-life is the time at which half of the excited atoms have undergone a quantum jump and emitted a photon. b. What is the half-life of the $3 p$ state of sodium?

Short Answer

Step by step solution

Part(a) Step 1: Given information

Part(a) Step 2: Simplify

Part(b) Step 1: Given information

Part(b) Step 2: Simplify

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a. Find an expression in terms of tfor the half-life t1/2 of a sample of excited atoms. The half-life is the time at which half of the excited atoms have undergone a quantum jump and emitted a photon. b. What is the half-life of the 3p state of sodium?

Short Answer

Step by step solution

Part(a) Step 1: Given information

Part(a) Step 2: Simplify

Part(b) Step 1: Given information

Part(b) Step 2: Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

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Study anywhere. Anytime. Across all devices.

a. Find an expression in terms of $t$ for the half-life t1/2 of a sample of excited atoms. The half-life is the time at which half of the excited atoms have undergone a quantum jump and emitted a photon. b. What is the half-life of the $3 p$ state of sodium?