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 moves from a lower energy level (n = 1) to a higher energy level (n = ∞), it absorbs energy. The energy required for this transition corresponds to the wavelength of light used.
2. Recall the relationship between energy and wavelength: The energy of a photon is inversely proportional to its wavelength, given by the equation \( E = \frac{hc}{\lambda} \), where \( h \) is Planck's constant, \( c \) is the speed of light, and \( \lambda \) is the wavelength.
3. Consider the implications of using light with a shorter wavelength: Since energy is inversely proportional to wavelength, a shorter wavelength means higher energy photons.
4. Analyze the effect of higher energy photons on the hydrogen atom: If the energy of the incoming photons exceeds the ionization energy of the hydrogen atom, the electron can be completely removed from the atom, resulting in ionization.
5. Conclude the outcome: Using light with a shorter wavelength than that required for the transition from n = 1 to n = ∞ will likely lead to ionization of the hydrogen atom, as the energy provided by the photons is sufficient to overcome the ionization energy.