Question

Ultraviolet light of wavelength 200 nm is shone on a clean metal surface, and the stopping voltage for photoemission of electrons is measured. When the incident wavelength is changed to 139 nm, the stopping potential is found to be twice its previous value. Calculate,
(a) The work function for this meal in eV, and (b) the stopping potential, if light of wavelength 180 nm is used, in eV

Answer 1

Answer:

We know that

$k = e - \phi = - v$

Where k is kinetic , e is incident , phi is work function and v is stopping voltage .

Since

$e = \frac{hc}{ \lambda} \\ \\ so \\ \\ \pink{ \frac{1}{ \lambda _{v} } = \frac{1}{\lambda _{ \phi} } - \frac{1}{\lambda _{e} } } \\ \\ given \: that \\ \\ \frac{1}{2\lambda _{v(200)} } = \frac{1}{\lambda _{v(139)} } \\ \\ \frac{1}{\lambda _{ \phi} } - \frac{1}{{200 } } = 2({ \frac{1}{\lambda _{ \phi} } - \frac{1}{{139 } } } ) \\ \\ \frac{1}{\lambda _{ \phi} } = \frac{2}{139} - \frac{1}{200} = \frac{400 - 139}{200 \times 139} \\ \\ {\lambda _{ \phi} } \approx \frac{200 \times 140}{260} \approx108 \: nm$

Second part of question use same formula

$\lambda _{ v} = \frac{180 \times 108}{180 - 108} = \frac{180 \times 108}{72} = 240 \: nm$

Now I hope you can find energies from these wave lengths .