The maximum kinetic energy of photoelectron is doubled when the wavelength of light incident on the photosensitive changes from `lambda_1` to `lambda_2`. Deduce expression for the threshold wavelength and work function for metals in terms of `lambda_1` and `lambda_2`

Explanation

Let `E_1=E,E_2=2E,E=hc(1/lamda-1/lamda_0)`
`E_1=hc(1/lamda-1/lamda_0)`
`E_2=hc(1/lamda-2/lamda_0)`
`hc(1/lamda_2-1/lamda_0)=2hc(1/lamda_1-1/lamda_0)`
`1/lamda_2-1/lamda_0=2/lamda_2-2/lamda_0`
`1/lamda_0=2/lamda_1-1/lamda_2`
`(2lamda_2-lamda_1)/(lamda_1lamda_2)=1/lamda_1`
`lamda_0=(lamda_1lamda_2)/(2lamda_2-lamda_1)`
Work function `=(hc)/lamda_0=(hc(2lamda_2-lamda_1))/(lamda_1lamda_1)`