Photoelectric emission is observed from a surface for frequencies `v_(1) "and" v_(2)` of the incident radiation `(v_(1) gt v_(2))` . If maximum kinetic energies of the photo electrons in the two cases are in the ratio `1:K` , then the threshold frequency is given by:

Explanation

In 1st case, K.E. `= h v_(1) - h v_(0) = h (v_(1) - v_(0))`
In 2nd case, K.E. `= h v_(2) - h v_(0) = h (v_(2) - v_(0))`
Given `(h (v_(1) - v_(0)))/(h(v_(2) - v_(0))) = (1)/(k) or v_(2) -v_(0) = k (v_(1) - v_(0)) = k v_(1) - kv_(0)`
or `k v_(0) - v_(0) = kv_(1) - v_(2) or v_(0) (k -1) = kv_(1) = v_(2) or v_(0) = (kv_(1) - v_(2))/(k -1)`