   Chapter 30, Problem 8CQ

Chapter
Section
Textbook Problem

What is a hydrogen-like atom, and how are the energies and radii of its electron orbits related to those in hydrogen?

To determine

A hydrogen-like atom, and also how the energies and radii of its electron orbits related to those in hydrogen?

Explanation

Given Data:

Given a hydrogen-like atom

Formula Used:

Radii of hydrogen −like atom is calculated as

rn=n2ZaB

Wherern= radius of nth orbit

Z= Number of protons in the nucleus

Energy of hydrogen-like atom is calculated as

En=Z2n2Eo

WhereEn= Energy of nth orbit

Z= Number of protons in the nucleus

Eo= Energy of ground state

Calculation:

Hydrogen-like atom are the atoms with only one electron and Z protons in its nucleus.

For hydrogen −like atom, radius is

rHydrogenlike=n2ZaB

For hydrogen atom,Z=1

Thus, radius is given as

rHydrogen=n21aB=n2aB

Thus, relation between the radius of hydrogen and hydrogen-like atom is given as

rHydrogen=1ZrHydrogenlike

Also, Energy of hydrogen-like atom is giv

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