Following results are observed when sodium metal is irradiated with different wavelengths. Calculate threshold wavelength.

Explanation

Let, threshold wavelength`=lamda_(0)nm=lamda_(0)xx10^(-9)m`
Again, Kinetic energy of emitted electron
`((1)/(2)mv^(2))=h(v-v_(0))=hc((1)/(lamda)-(1)/(lamda_(0)))` . . (1)
Putting the given values in (1) we get,
`(1)/(2)m (2.55xx10^(5))^(2)=(hc)/(10^(-9))((1)/(500)-(1)/(lamda_(0)))` . . . (2)
`(1)/(2)m(4.35xx10^(5))^(2)=(hc)/(10^(-9))((1)/(450)-(1)/(lamda_(0)))` . . .(3)
`(1)/(2)m(5.35xx10^(5))^(2)=(hc)/(10^(-9))((1)/(400)-(1)/(lamda_(0)))` . . . (4)
Dividing (3) by (2) we get, `(lamda_(0)-450)/(450lamda_(0))xx(500lamda_(0))/(lamda_(0)-500)=((4.35)/(2.55))^(2)`
or, `lamda_(0)=530.88cong 531`nm.