Question 187: Dual Nature of Matter and Radiation

Question

The magnetic field associated with a light wave is given, at the origin, by B = B
0
[sin(3.14 $$ 	imes $$ 10
7
)ct + sin(6.28 $$ 	imes $$ 10
7
)ct]. If this light falls on a silver plate having a work function of 4.7 eV, what will be the maximum kinetic energy of the photo electrons ?
(Take c = 3 $$ 	imes $$ 10
8
ms
$$-$$1
, h = 6.6 $$ 	imes $$ 10
$$-$$34
J-s)

Accepted Answer

Given that,
B = B
0
[sin (3.14 $$ 	imes $$ 10
7
) ct + sin(6.28 $$ 	imes $$ 10
7
) ct]
This light wave is non-monochromotic wave as here is two different frequency in the magnetic field.
Given work function ($$\phi $$) = 4.7 eV
Question says to find the maximum kinetic energy, so we have to use maximum frequency among the available frequency.
As,
K
max
= E
max
$$-$$ $$\phi $$
Emax = hF
= h $$ 	imes $$ $${\omega  \over {2\pi }}$$
= 6.6 $$ 	imes $$ 10
$$-$$34
$$ 	imes $$ $${{6.28 	imes {{10}^7} 	imes 3 	imes {{10}^8}} \over {2\pi }}$$
=  6.6$$ 	imes $$ 3 $$ 	imes $$ 10
$$-$$19
J
=  $${{6.6 	imes 3 	imes {{10}^{ - 19}}} \over {1.6 	imes {{10}^{ - 19}}}}eV$$
= 12.375 $$eV$$
$$ 	herefore $$  K
max
= 12.375 $$-$$ 4.7
= 7.675 $$eV$$
$$ \simeq $$  7.7 $$eV$$

Answer

6.82 eV

Answer

12.5 eV

Answer

8.52 eV

Answer

7.72 eV

Dual Nature of Matter and Radiation

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