An electron in hydrogen-like atom makes a transition from nth orbit or emits radiation corresponding to Lyman series. If de Broglie wavelength of electron in nth orbit is equal to the wavelength of rediation emitted , find the value of `n` . The atomic number of atomis `11`.

Explanation

To solve the problem step by step, we need to find the value of `n` for an electron in a hydrogen-like atom with atomic number `Z = 11` that emits radiation corresponding to the Lyman series. The de Broglie wavelength of the electron in the nth orbit is equal to the wavelength of the emitted radiation.

### Step 1: Understand the Lyman series
The Lyman series corresponds to transitions where the final energy level is n=1. The wavelength of radiation emitted during a transition from level n to level 1 can be expressed using the Rydberg formula:
\[ \frac{1}{\lambda} = Z^2 R \left(1 - \frac{1}{n^2}\right) \]
where \( R \) is the Rydberg constant.
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