A metal plate of work function `phi` is illuminated by a monochromatic light beam of wavelength `lamda` A singly ionised ion is fixed at a distance r from the metal plate such that electrons emitted from the metal plate often revolve around it. Calculate the maximum possible value of `lamda`.

Explanation

To solve the problem, we need to calculate the maximum possible wavelength (λ_max) of the light that can illuminate a metal plate with work function (φ) while allowing electrons emitted from the plate to revolve around a singly ionized ion fixed at a distance (r) from the plate.

### Step-by-Step Solution:

1. **Understand the Forces Involved**:
- The centripetal force required for the electron to revolve around the ion is provided by the electrostatic force of attraction between the electron and the singly ionized ion.
- The centripetal force (F_c) can be expressed as:
\[
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