EBK INQUIRY INTO PHYSICS
EBK INQUIRY INTO PHYSICS
8th Edition
ISBN: 8220103599450
Author: Ostdiek
Publisher: Cengage Learning US
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Chapter 11, Problem 4C
To determine

(a)

The size of aluminum-27 and compare it with the size of first Bohr orbit in hydrogen atom.

Expert Solution
Check Mark

Answer to Problem 4C

The size of aluminum-27 is compare it with the size of first Bohr orbit in hydrogen atom.

Explanation of Solution

Given info:

  • The size of first Bohr orbit in hydrogen atom is 5.29×1011m.
  • The Empirical formula is given to find the size of isotope.

Formula used:

Formula to find the size of isotope using formula of radius is,

V=43πr3V=43×3.14×(1.2×1015×A13)3V=7.238×1045×A

Here, A is the atomic mass, V is the volume of nucleus.

Calculation:

Substitute the given values to find the size of aluminum-27.

V=7.238×1045×39.96238=2.892×1043m3

Finding the size of first Bohr orbit:

V'=43πr'3V=43×3.14×(5.29×1011m)3V=6.2×1031m3

The size of first Bohr orbit in hydrogen atom is 3.175×1012 times more than the size of aluminum-27.

Conclusion:

Thus, the size of first Bohr orbit in hydrogen atom is 3.175×1012 times more than the size of aluminum-27.

To determine

(c)

To find the size of copper-63 and compare it with the size of first Bohr orbit in hydrogen atom.

Expert Solution
Check Mark

Answer to Problem 4C

The size of copper-63 is compare it with the size of first Bohr orbit in hydrogen atom.

Explanation of Solution

Given info:

  • The size of first Bohr orbit in hydrogen atom is 5.29×1011m.
  • The Empirical formula is given to find the size of isotope.

Formula used:

Formula to find the size of isotope using formula of radius is,

V=43πr3V=43×3.14×(1.2×1015×A13)3V=7.238×1045×A

Here,

A is the atomic mass, V is the volume of nucleus.

Calculation:

Substitute the given values to find the size of copper-63.

V=7.238×1045×62.92959=4.55×1043m3

Finding the size of first Bohr orbit:

V'=43πr'3V=43×3.14×(5.29×1011m)3V=6.2×1031m3

The size of first Bohr orbit in hydrogen atom is 1.36×1012 times more than the size of argon-40.

Conclusion:

Thus, the size of first Bohr orbit in hydrogen atom is 2.1435×1012 times more than the size of copper-63.

To determine

(d)

To find the size of cesium-134 and compare it with the size of first Bohr orbit in hydrogen atom.

Expert Solution
Check Mark

Answer to Problem 4C

The size of cesium-134 is compare it with the size of first Bohr orbit in hydrogen atom.

Explanation of Solution

Given info:

  • The size of first Bohr orbit in hydrogen atom is 5.29×1011m.
  • The Empirical formula is given to find the size of isotope.

Formula used:

Formula to find the size of isotope using formula of radius is,

V=43πr3V=43×3.14×(1.2×1015×A13)3V=7.238×1045×A

Here, A is the atomic mass, V is the volume of nucleus.

Calculation:

Substitute the given values to find the size of cesium-134.

V=7.238×1045×133.9067=9.691×1043m3

Finding the size of first Bohr orbit:

V'=43πr'3V=43×3.14×(5.29×1011m)3V=6.2×1031m3

The size of first Bohr orbit in hydrogen atom is 6.4×1011 times more than the size of cesium-134.

Conclusion:

Thus, the size of first Bohr orbit in hydrogen atom is 6.4×1011 times more than the size of cesium-134.

To determine

(d)

The size of bismuth-211 and compare it with the size of first Bohr orbit in hydrogen atom.

Expert Solution
Check Mark

Answer to Problem 4C

The size of bismuth-211 is compare it with the size of first Bohr orbit in hydrogen atom.

Explanation of Solution

Given info:

  • The size of first Bohr orbit in hydrogen atom is 5.29×1011m
  • The Empirical formula is given to find the size of isotope.

Formula used:

Formula to find the size of isotope using formula of radius is,

V=43πr3V=43×3.14×(1.2×1015×A13)3V=7.238×1045×A

Here, A is the atomic mass, V is the volume of nucleus.

Calculation:

Substitute the given values to find the size of bismuth-211.

V=7.238×1045×210.98726=1.527×1042m3

Finding the size of first Bohr orbit:

V'=43πr'3V=43×3.14×(5.29×1011m)3V=6.2×1031m3

The size of first Bohr orbit in hydrogen atom is 4.06×1011 times more than the size of bismuth-211.

Conclusion:

Thus, the size of first Bohr orbit in hydrogen atom is 4.06×1011 times more than the size of bismuth-211.

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