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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

A proton is confined within an atomic nucleus of diameter $4.0 m$ . Use a one-dimensional model to estimate the smallest range of speeds you might find for a proton in the nucleus.

The probability density for an electron that has passed through an experimental apparatus. If $1.0 \times 10^{6}$ electrons are used, what is the expected number that will land in alocalid="1649312933417" $0.010 m m$ wide strip atlocalid="1649312941736" $(a) x = 0.000 m m$ and localid="1649312949893" $(b) 2.000 m m$ ?

A 1.0-mm-diameter sphere bounces back and forth between two walls at $x = 0 mm$ and $x = 100 mm$ . The collisions are perfectly elastic, and the sphere repeats this motion over and over with no loss of speed. At a random instant of time, what is the probability that the center of the sphere is

a. At exactly $x = 50.0 mm$ ?

b. Between $x = 49.0 mm$ and $x = 51.0 mm$ ?

c. At $x \geq 75 mm$ ?

Consider the electron wave function

$ψ (X) = \{\begin{cases} c \sin (\frac{2 πx}{L}) 0 \leq x \leq L \\ 0 x < 0 o r x > L \end{cases}$

a. Determine the normalization constant c. Your answer will be in terms of L.

b. Draw a graph of $ψ (x)$ over the interval -L $\leq$ x $\leq$ 2L.

c. Draw a graph of ${|ψ (x)|}^{2}$ over the interval -L $\leq$ x $\leq$ 2L. d. What is the probability that an electron is in the interval 0 $\leq$ x $\leq$ L/3?

Consider the electron wave function

$ψ (x) = \{\begin{cases} c x |x| \leq 1 n m \\ \frac{c}{x} |x| \geq 1 n m \end{cases}$

where x is in nm.

a. Determine the normalization constant c.

b. Draw a graph of $ψ (x)$ over the interval role="math" localid="1650907186096" $- 5 n m \leq x \leq 5 n m$ .

Provide numerical scales on both axes.

c. Draw a graph of ${|ψ (x)|}^{2}$ over the interval role="math" localid="1650907657944" $- 5 n m \leq x \leq 5 n m$ .

Provide numerical scales.

d. If $10^{6}$ electrons are detected, how many will be in the interval

role="math" localid="1650908765290" $- 1.0 n m \leq x \leq 1.0 n m$ ?

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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

Step by step solution

the smallest one-dimensional box

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Most popular questions from this chapter

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