Determine the maximum wavelength of incident radiation that can be used to remove the remaining electron from a singly ionized helium atom He⁺ (Z = 2). Assume the electron is in its ground state. A)6.2 nm B)12.4 nm C)22.8 nm D)45.6 nm E)54.4 nm

Question

Quizplus · Accepted Answer

To remove the remaining electron, we need to excite it from its ground state to the ionization state. This means we need to supply enough energy to overcome the ionization potential, which is given by:

IP = -Rhc(Zeff)^2/n^2

Where R is the Rydberg constant, h is Planck's constant, c is the speed of light, Zeff is the effective nuclear charge, n is the principal quantum number of the electron's initial (ground state) level, and IP is the ionization potential.

For singly ionized helium, Zeff = 1, n = 1, and IP = 24.6 eV. Solving for the maximum wavelength of incident radiation that can supply this energy:

E = hc/lambda = IP

lambda = hc/IP = (6.626 x 10^-34 J.s)(2.998 x 10^8 m/s)/(24.6 eV x 1.602 x 10^-19 J/eV)

lambda = 22.8 nm

Therefore, the maximum wavelength of incident radiation that can remove the remaining electron from a singly ionized helium atom in its ground state is 22.8 nm. The correct answer is choice C.

Determine the Maximum Wavelength of Incident Radiation That Can Be