The first excitation potential of a hypotheticalhydrogen-like atom is 15 V. Find the third excitationpotential of the atom

The excitation potential of a hydrogen-like atom is given by the formula:

V = 13.6 * (1/n1² - 1/n2²)

where n1 and n2 are the initial and final energy levels respectively.

For the first excitation potential, the atom moves from the ground state (n1 = 1) to the first excited state (n2 = 2). So, we can write:

15 = 13.6 * (1/1² - 1/2²)

Solving this equation, we find that the constant 13.6 is equal to 15.

For the third excitation potential, the atom moves from the ground state (n1 = 1) to the third excited state (n2 = 4). So, we can write:

V = 15 * (1/1² - 1/4²)

Solving this equation, we find that the third excitation potential V is approximately 13.125 V.