From Einstein's photoelectric equation, the maximum kinetic energy of emitted photoelectrons is given by:
Kmax=λhc−Φ
where λ is the wavelength of incident radiation and Φ is the work function of the metal.
The work function is related to the threshold frequency ν0 by Φ=hν0. From the given graph, the x-intercept represents the threshold frequency. We can observe that:
ν0(X1)<ν0(X2)<ν0(X3)
Therefore, the work functions of the metals follow the order:
Φ(X1)<Φ(X2)<Φ(X3)
For the same wavelength λ of incident radiation, the term λhc is constant. Thus, the kinetic energy Kmax will be greatest for the metal with the smallest work function.
Since metal X1 has the minimum work function, it will emit electrons with the greatest kinetic energy.
Answer: X1
