Photoelectric emission is observed from a surface for frequencies `v_(1) and v_(2)` of incident radiations
`(v_(1) gt v_(2))`. If the maximum kinetic energy of photoelectrons in the two cases are in the ratio of `2 : 1` then threshold frequency `v_(0)` is given by.

Explanation

To solve the problem, we will use the principles of the photoelectric effect and the relationships between the kinetic energy of emitted electrons and the frequencies of the incident light.

### Step-by-Step Solution:

1. **Understanding the Photoelectric Effect**:
The photoelectric effect states that when light of sufficient frequency strikes a metal surface, it can eject electrons. The relationship between the frequency of the incident light (ν) and the kinetic energy (KE) of the emitted electrons is given by Einstein's photoelectric equation:
\[
KE = h\nu - h\nu_0
...