Ultraviolet light of wavelength `2271Å` from a 100W mercury source irradiates a photocell made of molybdenum metal. If the stopping potential is 1.3V, estimate the work function of the metal. How would the photocell respond to a high intensity `(~10^(5)Wm^(-2))` red light of wave length `6328Å` produced by a He-Ne laser?

Explanation

Given , wavelength , `lamda = 2,271Å`
Frequency , `v=c/lamda=(3xx10^8)/(2,271xx10^(-10))Hz`
Power , P = 100 W
Stopping potential , `V_0=1.3V`
Then
`hv=1/2mv^2+W_0`
where `W_0` is the work function of metal
`:. W_0=hv-eV_0=(hc)/lamda-eV_0[:.1/2mv^2=eV_0]`
`=(6.63xx10^(-34)xx3xx10^(8))/(2,271xx10^(-10))-1.6xx10^(-19)xx1.3`
`=6.67xx10^(-19)J - 4.17eV`
Threshold frequency is given by
`v_0=W_0/h=(6.67xx10^(-19))/(6.63xx10^(-34))`
`=1.0xx10^(15)Hz.`
Now, for red light
Wavelength , `lamda_r=6,328Å`
`implies` Frequency , `v_r=c/lamda=(3xx10^8)/(6,328xx10^(-10))`
`=4.74xx10^(14)Hz`.
As `vlt v_0`
The photocell will not respond to this frequency howsoever high be the intensity of laser light .