Calculate the maximum wavelength of light capable of removing an electron for a hydrogen atom fr

step 1 Okay, so for an electron in n equals 1, we have the equation delta E equals negative 2 .17 times

Calculate the maximum wavelength of light capable of...

Key Concepts

Hydrogen Atom Energy Levels

The hydrogen atom has discrete energy levels characterized by the principal quantum number n. The energy of an electron in a hydrogen atom is given by a formula that depends inversely on the square of n. This quantization means that electrons can only occupy specific energy levels, with the ground state (n=1) being the most tightly bound and excited states (such as n=2) having higher (less negative) energy values.

Ionization Energy

Ionization energy is the minimum energy required to remove an electron completely from its bound state in an atom. For hydrogen, this energy is determined by the difference between the electron's current energy level and the energy level at infinity (usually taken as zero). The ionization energy differs depending on whether the electron is in the ground state or an excited state, with the value being lower for electrons in higher energy levels.

Photon Energy and Wavelength Relationship

The energy of a photon is inversely proportional to its wavelength, as described by the equation E = hc/?, where h is Planck’s constant and c is the speed of light. This relationship implies that a photon must have a wavelength below a certain maximum value (or equivalently, an energy above a minimum threshold) in order to provide sufficient energy to ionize an atom.

Quantum Numbers

Quantum numbers, such as the principal quantum number n, describe the properties of electrons in atoms. They determine the energy, angular momentum, and spatial distribution of an electron's probability density. In the context of ionization, the principal quantum number is particularly important because it directly impacts the binding energy of the electron and hence the energy required to remove it.

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