Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

For what value of the principal quantum number n would the effective radius, as shown in a probability density dot plot for the hydrogen atom, be 1.00 mm? Assume that has its maximum value of n-1. (Hint:See Fig.39-24.)

The value of principal quantum number is $4.3 \times 10^{3}$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Identification of the given data:

The given data is listed below as,

Radius of hydrogen atom is $r = 1.00 mm = 1.00 \times 10^{- 3} m$

Step 2: The principal Quantum number:

The principal quantum number is used to describe the electron’s state and is the one four quantum number assigned to each electron in an atom.

The value of the principal quantum number is natural number.

Step 3: Determine the value of principal quantum number:

According to the fig. 39-24. the principal quantum number satisfies,

$r = n^{2} a$

Here, the Bohr radius is $a = 5.29 \times 10^{- 13} m$ .

Solving the above equation will give the value of the principal quantum number is,

$n = \sqrt{\frac{r}{a}}$

Substitute $1.00 \times 10^{- 3} m$ for r in the above equation.

$n = \sqrt{\frac{1.00 \times 10^{- 3} m}{5.29 \times 10^{- 13} m}} = 4.3 \times 10^{3}$

Hence, the value of principal quantum number is $4.3 \times 10^{3}$ .

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Fundamentals Of Physics

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Short Answer

For what value of the principal quantum number n would the effective radius, as shown in a probability density dot plot for the hydrogen atom, be 1.00 mm? Assume that has its maximum value of n-1. (Hint:See Fig.39-24.)

Step by Step Solution

Step 1: Identification of the given data:

Step 2: The principal Quantum number:

Step 3: Determine the value of principal quantum number:

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Fundamentals Of Physics

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Short Answer

For what value of the principal quantum number n would the effective radius, as shown in a probability density dot plot for the hydrogen atom, be 1.00 mm? Assume that has its maximum value of n-1. (Hint:See Fig.39-24.)

Step by Step Solution

Step 1: Identification of the given data:

Step 2: The principal Quantum number:

Step 3: Determine the value of principal quantum number:

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