Question 235: Dual Nature of Matter and Radiation

Question

The surface of a metal is illuminated alternately
with photons of energies E
1
= 4 eV and E
2
= 2.5 eV
respectively. The ratio of maximum speeds of the
photoelectrons emitted in the two cases is 2. The
work function of the metal in (eV) is _____.

Accepted Answer

Given,
E
1
= 4 eV
E
2
= 2.5 eV
and $${{{{\left( {{V_1}} ight)}_{\max }}} \over {{{\left( {{V_2}} ight)}_{\max }}}} = 2$$
$${{{1 \over 2}m{{\left( {{{\left( {{V_1}} ight)}_{\max }}} ight)}^2}} \over {{1 \over 2}m{{\left( {{{\left( {{V_2}} ight)}_{\max }}} ight)}^2}}} = {{{E_1} - {\phi _0}} \over {{E_2} - {\phi _0}}}$$
$$ \Rightarrow $$ $${{{{\left( {{{\left( {{V_1}} ight)}_{\max }}} ight)}^2}} \over {{{\left( {{{\left( {{V_2}} ight)}_{\max }}} ight)}^2}}} = {{4 - {\phi _0}} \over {2.5 - {\phi _0}}}$$
$$ \Rightarrow $$ $${\left( 2 ight)^2} = {{4 - {\phi _0}} \over {2.5 - {\phi _0}}}$$
$$ \Rightarrow $$ 10 - 4$$\phi $$
0
= 4 - $$\phi $$
0
$$ \Rightarrow $$ 3$$\phi $$
0
= 6
$$ \Rightarrow $$ $$\phi $$
0
= 2
$$ 	herefore $$ Work function($$\phi $$) of the metal = 2 eV

Dual Nature of Matter and Radiation

The surface of a metal is illuminated alternately with photons of energies E 1 = 4 eV and E 2 = 2.5 eV respectively. The ratio of maximum speeds of the photoelectrons emitted in the two cases is 2. The work function of the metal in (eV) is _____.

Integer / Numeric Answer Type