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Chapter 30: Q11PE (page 1112)

If a hydrogen atom has its electron in the n = 4 state, how much energy in eV is needed to ionize it?

Short Answer

Expert verified

The energy needed to ionize hydrogen atom is 0.85 eV.

Step by step solution

01

Definition of ionisation energy

The energy that is enough to separate the electron in the last shell of the atom also called valance electron is the ionization energy.

02

Given information and formula to be used

Consider the hydrogen atom has 4 states.

Consider the formula for the ionization energy as follows:

\({E_n} = \frac{{13.6\;{\rm{eV}}}}{{{n^2}}}\)

Here, \({E_n}\) is the ionization energy and nis the energy level.

03

Determine the energy in eV needed to ionize the hydrogen atom which has its electron in the n=4 state. 

Substitute 4 for nand determine the ionisation energy.

\(\begin{array}{c}{E_n} = \frac{{13.6\;{\rm{eV}}}}{{{4^2}}}\\{E_n} = \frac{{13.6\;{\rm{eV}}}}{{16}}\\{E_n} = 0.85\;{\rm{eV}}\end{array}\)

Therefore, the energy needed to ionize hydrogen atom is 0.85 eV.

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Most popular questions from this chapter

Explain why characteristic x rays are the most energetic in the EM emission spectrum of a given element.

The wavelength of the four Balmer series lines for hydrogen are found to be 410.3, 434.2, 486.3, and 656.5 nm. What average percentage difference is found between these wavelength numbers and those predicted by\[\frac{{\bf{1}}}{{\bf{\lambda }}}{\bf{ = R}}\left( {\frac{{\bf{1}}}{{{\bf{n}}_{\bf{f}}^{\bf{2}}}}{\bf{ - }}\frac{{\bf{1}}}{{{\bf{n}}_{\bf{i}}^{\bf{2}}}}} \right){\bf{?}}\]It is amazing how well a simple formula (disconnected originally from theory) could duplicate this phenomenon.

Integrated Concepts

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