The energy needed to detach the electron of a hydrogen like ion in ground state is a system(a) what is the wavelength of the radiation emitted when the electron jumps from the first excited state to the ground state? (b) What is the radius of the orbit for this atom?

Explanation

To solve the given problem step by step, we will break it down into two parts as per the question.

### Part (a): Wavelength of the Radiation Emitted

1. **Identify the Energy in Ground State**:
The energy needed to detach the electron of a hydrogen-like ion in the ground state is given as \(4 \text{ Rydberg}\).
\[
E_1 = 4 \times 13.6 \text{ eV} = 54.4 \text{ eV}
...