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Chapter 34: Problem 27

What's the maximum wavelength of light that can ionize hydrogen in its ground state? In what spectral region is this?

Short Answer

Expert verified
The maximum wavelength of light that can ionize hydrogen in its ground state can be calculated using energy equations and is usually found within the ultraviolet region of the spectrum.

Step by step solution

01

Convert energy from eV to Joules

Ionization energy of hydrogen is 13.6 eV. This needs to be converted to joules as follows: 1 eV is equivalent to \(1.60219 \times 10^{-19}\) joules, therefore, the ionization energy in joules is \(13.6 \times 1.60219 \times 10^{-19}\) joules.
02

Calculate the wavelength

The energy of a photon is given by the equation \(E=hc/\lambda\), where \(h\) is Planck's constant \((6.62607004 \times 10^{-34} m^2kg/s)\), \(c\) is the speed of light \((299,792,458 m/s)\), and \(\lambda\) is the wavelength. Rearranging for \(\lambda\), we have \(\lambda=hc/E\). Substituting the values gives the wavelength that can ionize hydrogen.
03

Identify the Spectral Region

Given the calculated wavelength, the spectral region can be identified through the reference to standard electromagnetic wave tables. Wavelengths can fall into categories which range from radio waves (the longest) to gamma waves (the shortest).

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