Final answer:
The ratio of the area within the electron orbits for the first excited state to the ground state in a hydrogen atom is 16:1, based on the Bohr model.
Step-by-step explanation:
The ratio of the area within the electron orbits for the first excited state to the ground state for the hydrogen atom can be determined from the Bohr model of the hydrogen atom.
In the Bohr model, the radius of an electron orbit is proportional to n², where n is the principal quantum number. The area of a circle (which the orbit can be approximated to) is given by πr². Since the radius is proportional to n², the area is therefore proportional to n⁴.
For the ground state (n=1), the area is proportional to 1⁴, and for the first excited state (n=2), it is proportional to 2⁴ or 16. Hence, the ratio of the area within the electron orbits for the first excited state to the ground state is 16:1.