Why is the electron in a Bohr hydrogen atom bound less tightly when it has a quantum number of 3 than when it has a quantum number of 1?

Answer: An electron having a quantum number of one is closer to the nucleus

Explanation:

The Bohr model relies on electrostatic attraction between the nucleus and orbital electron. Hence, the closer an electron is to the nucleus the more closely it is held by the nucleus and the lesser its energy (the more stable the electron is and the more difficult it is to ionize it). The farther an electron is from the nucleus (in higher shells or energy levels), the less the electrostatic attraction of such electron to the nucleus due to shielding effect. Hence it is less tightly held.

Below.

Explanation:

1. At quantum number 3 it is further from the positive protons in the nucleus.

2. The inner electrons have a shielding effect on the attraction from the protons in the nucleus.