A certain, metallic surface is illuminated with monochromatic light of wavelength, `lamda`. The stopping potential for photoelectric current for this light is `3 V_(0)`. If the same surface is illuminated with light of wavelength `2lamda`, the stopping potential is `V_(0)`. The threshold wavelength for this surface for photoelectric effect is

Options

A. `6 lamda`
B. `4 lamda`
C. `(lamda)/(4)`
D. `(lamda)/(6)`

Answer

B

Explanation

`eV_(0) = h (f - f_(0))`
or, `eV_(0) = h ((c)/(lamda) - f_(0))` [`f_(0)=` threshold frequency]
In the firstt case,
`e.3V_(0) = h ((c)/(lamda) - f_(0))`…(1)
In the second case,
`eV_(0) = h ((c)/(2lamda) - f_(0))`...(2)
Dividing equation (1) by equation (2),
`3 = ((c)/(lamda) - f_(0))/((c)/(2lamda)- f_(0))`
or, `(c)/(lamda) -f_(0) = (3)/(2).(c)/(lamda) - 3f_(0)`
or, `2f_(0) = (1)/(2) (c)/(lamda) or, f_(0) = (c)/(4lamda)`
`:.` Threshold wavelength, `lamda_(0) = (c)/(f_(0)) = 4lamda`