Final answer:
The statement that (13.6 eV)/(hc) equals 1.097 × 10⁷ m, which is Rydberg's constant, is true. This can be confirmed by substituting the energy equivalent of 1 eV and the values of Planck's constant and the speed of light into the expression. The correct option is A.
Step-by-step explanation:
The student has asked to show that (13.6 eV)/(hc) = 1.097 × 10⁷ m, which is equivalent to Rydberg's constant. Using the given energy equivalent of 13.6 eV for the ionization energy of hydrogen and the values for Planck's constant (h) and the speed of light (c), we can calculate this expression.
Rydberg's constant (R) is related to the energy levels of electrons in a hydrogen atom and is a fundamental constant in atomic physics. To confirm the equation, we can use the energy equivalent of 1 eV = 1.602 x 10-19 J and the constants h = 6.626 x 10-34 Js and c = 2.998 x 108 m/s to find that (13.6 eV)/(hc) does indeed yield a value numerically equal to 1.097 × 10⁷ m-1.