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Chapter 39: Q.41 (page 1139)

What is the smallest one-dimensional box in which you can confine an electron if you want to know for certain that the electron’s speed is no more than 10 m/s?

Short Answer

Expert verified

The probability density of the electron in a hydrogen

Step by step solution

the smallest one-dimensional box

When $r = 0.763 a x p_{r (r) = (2)} \frac{{(0.763 a_{x})}^{2}}{{a^{2}}_{n}} [1 - \frac{0.763 a x}{2 πa}] = \frac{0.2076}{a_{x}}$

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Most popular questions from this chapter

Consider the electron wave function

$ψ (X) = \{\begin{cases} 0 x < 0 n m \\ (1.414 n m^{- \frac{1}{2}}) e^{- \frac{x}{(1.0 n m)}} x \geq 0 n m \end{cases}$

where x is in cm.

a. Determine the normalization constant c.

b. Draw a graph of c1x2 over the interval -2 cm $\leq$ x $\leq$ 2 cm. Provide numerical scales on both axes.

c. Draw a graph of 0 c1x2 0 2 over the interval -2 cm $\leq$ x $\leq$ 2 cm. Provide numerical scales.

d. If 104 electrons are detected, how many will be in the interval 0.00 cm $\leq$ x $\leq$ 0.50 cm?

FIGURE P39.32 shows $| ψ (x) |^{2}$ for the electrons in an experiment.

a. Is the electron wave function normalized? Explain.

b. Draw a graph of $ψ (x)$ over this same interval. Provide a numerical scale on both axes. (There may be more than one acceptable answer.)

c. What is the probability that an electron will be detected in a $0.0010 - cm$ -wide region at $x = 0.00 cm$ ? At $x = 0.50 cm$ ? At $x = 0.999 cm ?$

d. If $10^{4}$ electrons are detected, how many are expected to land in the interval $- 0.30 cm \leq x \leq 0.30 cm$ ?

What is the difference between the probability and the probability density?

A pulse of light is created by the superposition of many waves that span the frequency range $f_{0} - \frac{1}{2} Δ f \leq f \leq f_{0} + \frac{1}{2} Δ f$ , wherc $f_{0} = c / λ$ is called thc center frequency of thc pulsc. Lascr technology can generate a pulse of light that has a wavelength of $600 nm$ and lasts a mere $6.0$ fs $1 fs = 1$ femtosecond localid="1650804865678" $= 10^{- 15} s)$ .

a. What is the center frequency of this pulse of light?

b. How many cycles, or oscillations, of the light wave are completed during the $6.0$ fs pulse?