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Chapter 41: Q. 19 (page 1207)

An excited state of an atom has a $25 n s$ lifetime. What is the probability that an excited atom will emit a photon during a $0.50 n s$ interval?

Short Answer

Expert verified

The probability that an excited atom will emit a photon during a $0.50 n s$ interval is $0.20 %$

Step by step solution

01

Given Information

We need to find the probability that an excited atom will emit a photon during a $0.50 n s$ interval.

02

Simplify

Consider :

$τ = 25 n s ∆ t = 0.50 n s$

Using formula:

$∆ t = r ∆ t$ .

First, finding the decay rate:

$r = \frac{1}{τ} r = \frac{1}{25 n s} r = 0.040 n s^{- 1}$

Now, find prob decay $∆ t$ :

$∆ t = r \times ∆ t ∆ t = (0.040 n s^{- 1}) (0.50 n s) ∆ t = 0.02 \approx 0.2 %$

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Most popular questions from this chapter

Three electrons are in a one-dimensional rigid box (i.e., an infinite potential well) of length $0.50 n m$ . Two are in the $n = 1$ state and one is in the $n = 6$ state. The selection rule for the rigid box allows only those transitions for which $∆ n$ is odd.

a. Draw an energy-level diagram. On it, show the filled levels and show all transitions that could emit a photon.

b. What are all the possible wavelengths that could be emitted by this system?

FIGURE Q $41.5$ shows the outcome of a Stern-Gerlach experiment with atoms of element $X$ .

a. Do the peaks represent different values of the atom’s total angular momentum or different values of the $z -$ component of its angular momentum? Explain.

b. What angular momentum quantum numbers characterize these four peaks?

There exist subatomic particles whose spin is characterized by $s = 1$ , rather than the $s = \frac{1}{2}$ of electrons. These particles are said to have a spin of one.

a. What is the magnitude (as a multiple ofrole="math" localid="1650369219275" $♄$ ) of the spin angular momentum $S$ for a particle with a spin of one?

b. What are the possible values of the spin quantum number?

c. Draw a vector diagram similar to Figure 41.13 to show the possible orientations of $\vec{S}$ .

Consider the three hydrogen-atom states $6 p, 5 d$ and $4 f$ . Which has the highest energy?

What is the probability of finding a $1 s$ hydrogen electron at distance $r > a_{B}$ from the proton?

See all solutions

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