Question

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

Short answer

The difference between the distance of the 1^st quantum number and the nucleus is way lesser than that between the 3^rd quantum number and the nucleus. Hence, the force of attraction is more in 1^st quantum number than in 3^rd towards the nucleus

Step-by-step solution

elaborating what are quantum numbers

Quantum numbers are the values used to describe discrete energy levels of an atom or molecule. An atom can have four quantum numbers which describe its state and level of energy.

describing 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

We can observe that 1 quantum number is closer to the nuclear in comparison to the third quantum number. this means that difference between the distance of the 1^st quantum number and the nucleus is way lesser than that between the 3^rd quantum number and the nucleus. Hence, theforce of attraction is more in the 1^st quantum number than in the 3^rd towards the nucleus. So, the electron in a Bohr’s hydrogen atom is bound less tightly when it has a quantum number of 3 than when it has a quantum number of.