Question 382: Dual Nature of Matter and Radiation

Question

A metal surface is illuminated by light of two different wavelengths 248 nm and 310 nm. The maximum speeds of the photoelectrons corresponding to these wavelengths are u
1
and u
2
, respectively. If the ratio u
1
: u
2
= 2 : 1 and hc = 1240 eV nm, the work function of the metal is nearly

Accepted Answer

From Einstein's photoelectric equation,
kinetic energy of photoelectrons,
$$K = {1 \over 2}m{v^2} = {{hc} \over \lambda } - \phi $$ ..... (i)
For $$\lambda$$ = 248 nm, v = u
1
$$	herefore$$ $${K_1} = {1 \over 2}mu_1^2 = {{hc} \over {248}} - \phi $$ ...... (ii)
For $$\lambda$$ = 310 nm, v = u
2
$$	herefore$$ $${K_2} = {1 \over 2}mu_2^2 = {{hc} \over {310}} - \phi $$ ....... (iii)
Divide eqn. (ii) by eqn. (iii),
$${{u_1^2} \over {u_2^2}} = {{{{hc} \over {248}} - \phi } \over {{{hc} \over {310}} - \phi }} = {{{{1240} \over {248}} - \phi } \over {{{1240} \over {310}} - \phi }}$$
$$ \Rightarrow {\left( {{2 \over 1}} ight)^2} = {{5 - \phi } \over {4 - \phi }}$$
$$ \Rightarrow 16 - 4\phi  = 5 - \phi  \Rightarrow 3\phi  = 11$$
or, $$\phi$$ = 3.67 eV $$\approx$$ 3.7 eV

Answer

3.7 eV

Answer

3.2 eV

Answer

2.8 eV

Answer

2.5 eV

Dual Nature of Matter and Radiation

A metal surface is illuminated by light of two different wavelengths 248 nm and 310 nm. The maximum speeds of the photoelectrons corresponding to these wavelengths are u 1 and u 2 , respectively. If the ratio u 1 : u 2 = 2 : 1 and hc = 1240 eV nm, the work function of the metal is nearly

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