Consider a transition in which the electron of a hydrogen atom is excited from n = 1 to n = ∞.  (c) What will occur if light with a shorter wavelength than that in part (b) is used to excite the hydrogen atom?

Verified step by step guidance

1. Understand the concept of electron transitions in a hydrogen atom: When an electron in a hydrogen atom absorbs energy, it can move from a lower energy level (n = 1) to a higher energy level (n = ∞). This is known as an excitation process.
2. Recall that the energy of a photon is inversely proportional to its wavelength, as described by the equation: \( E = \frac{hc}{\lambda} \), where \( E \) is the energy, \( h \) is Planck's constant, \( c \) is the speed of light, and \( \lambda \) is the wavelength.
3. If light with a shorter wavelength than that used in part (b) is used, it means the light has higher energy because shorter wavelengths correspond to higher energy photons.
4. Consider the implications of using higher energy photons: If the energy of the incoming photon is greater than the energy required to excite the electron from n = 1 to n = ∞, the excess energy can ionize the hydrogen atom, completely removing the electron from the atom.
5. Conclude that using light with a shorter wavelength (higher energy) than necessary for the transition to n = ∞ can result in ionization of the hydrogen atom, as the electron is given enough energy to escape the attraction of the nucleus entirely.

Key Concepts

Quantum Energy Levels

In quantum mechanics, electrons in an atom occupy discrete energy levels, denoted by quantum numbers (n). For hydrogen, these levels are quantized, meaning an electron can only exist in specific states. The transition from a lower level (n=1) to a higher level (n=∞) represents ionization, where the electron is completely removed from the atom.

Photon Energy and Wavelength

The energy of a photon is inversely related to its wavelength, described by the equation E = hc/λ, where E is energy, h is Planck's constant, c is the speed of light, and λ is the wavelength. Shorter wavelengths correspond to higher energy photons, which can provide sufficient energy to excite electrons to higher energy levels or even ionize them.

Ionization Energy

Ionization energy is the minimum energy required to remove an electron from an atom in its gaseous state. For hydrogen, this energy corresponds to the transition from n=1 to n=∞. If light with a shorter wavelength than that used in part (b) is applied, it will have higher energy than the ionization energy, resulting in the complete removal of the electron from the hydrogen atom.