Question
The photoelectric work function for a metal surface is $$4.125\,eV.$$ The cut-off wavelength for this surface is
A.
$$4125\,\mathop {\text{A}}\limits^ \circ $$
B.
$$3000\,\mathop {\text{A}}\limits^ \circ $$
C.
$$6000\,\mathop {\text{A}}\limits^ \circ $$
D.
$$2062.5\,\mathop {\text{A}}\limits^ \circ $$
Answer :
$$3000\,\mathop {\text{A}}\limits^ \circ $$
Solution :
The minimum wavelength below which no photoelectron can emit from metal surface is called cut-off wavelength or threshold wavelength and is given by
$$\eqalign{
& {\text{Work function}} = \frac{{hc}}{{{\text{cut - off wavelength}}}} \cr
& {\text{or}}\,\,{\text{cut - off wavelength}} = \frac{{hc}}{{{\text{work}}\,{\text{function}}}} \cr
& \therefore {\lambda _0} = \frac{{hc}}{{{W_0}}}\,.......\left( {\text{i}} \right) \cr
& {\text{Given,}}\,h = 6.6 \times {10^{ - 34}}\,J - s \cr
& c = 3 \times {10^8}m/s \cr
& {W_0} = 4.125\,eV \cr
& = 4.125 \times 1.6 \times {10^{ - 19}}\,J \cr} $$
Substituting the given values in Eq. (i), we get
$$\eqalign{
& {\lambda _0} = \frac{{6.6 \times {{10}^{ - 34}} \times 3 \times {{10}^8}}}{{4.125 \times 1.6 \times {{10}^{ - 19}}}}\,\mathop {\text{A}}\limits^ \circ \cr
& = 3 \times {10^{ - 7}}m \cr
& = 3000\,\mathop {\text{A}}\limits^ \circ \cr} $$