The energy needed to detach the electron of a hydrogen like ion in ground state is a 4 Rydberg. (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 problem step by step, we will address both parts of the question: (a) finding the wavelength of the radiation emitted when the electron jumps from the first excited state to the ground state, and (b) calculating the radius of the orbit for the atom.

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

1. **Identify the Energy Levels**:
- The energy of the ground state (n=1) is given as \( E_1 = -4 \times 13.6 \, \text{eV} = -54.4 \, \text{eV} \).
- The energy of the first excited state (n=2) can be calculated using the formula:
\[
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