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Chapter 38: Q. 32 (page 1115)

How much energy does it take to ionize a hydrogen atom that is in its first excited state?

Short Answer

Expert verified

The excited hydrogen atom's ionization energy will be 3.4 eV or less.

Step by step solution

01

Given information

The given energy of the first excited state of a hydrogen atom

02

Finding ionization energy of hydrogen

The energy of an electron in a quantum state is calculated as follows:

En=-13.6eVn2

For the first excited state, the quantum number n is given by n=2. Hence the energy of the electron in the first excited state is

E2=-13.6eV22=-3.4eV

The energy of the electron after ionization is

Eion=0

As a result, the energy we must provide is

螖E=Eion-E2=0-(-3.4eV)=3.4eV

As a result, ionizing a hydrogen atom from its first excited state will require 3.4 eV of energy.

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