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In a photoelectric effect experiment, electrons are ejected from a titanium surface (work function, 3 eV) following irradiation with UV light. The energy of the incident UV light is 7.2 x 10-19 J.

(a) Calculate the wavelength of the ejected electrons.
(b) Calculate the wavelength of the incident UV light.
(c) would an iron surface (Ф-4.7 eV require a longer or shorter wavelength of light to eject electrons with the same wavelength calculated in part (a)? Briefly explain.

User Heb
by
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1 Answer

7 votes

Step-by-step explanation:

According to the Einstein law, it is known that


h * \\u = \phi + (1)/(2) mv^(2)

where, h = energy of light


\phi = work function


m v^(2) = kinetic energy of electron

It is given that the value of
h \\u is
7.2 * 10^(-19) J. And,

1 eV =
1.6 * 10^(-19) J

Here,
\phi for titanium is 4.33 eV

=
(4.33 * 1.6 * 10^(-19)) J

=
6.928 * 10^(-19) J

(a) First of all, kinetic energy will be calculated as follows.


(1)/(2)mv^(2) = h \\u - \phi

=
(7.2 * 10^(-19) - 6.92 * 10^(-19)) J

=
0.272 * 10^(-19) J

It is known that mass of electrons is equal to
9.109 * 10^(-31) kg.

Therefore,
mv^(2) = 0.544 * 10^(-19) J

and,
(mv)^(2) = 9.109 * 0.544 * 10^(-19) * 10^(-31)

=
4.955 * 10^(-50)

mv =
2.225 * 10^(-25)

Now, the relation between wavelength and mv is as follows.


\lambda = (6.626 * 10^(-34))/(2.225 * 10^(-25))

=
2.98 * 10^(-9) m

Therefore, the wavelength of the ejected electrons is
2.98 * 10^(-9) m.

(b) It is known that relation between energy and wavelength is as follows.

E =
h \\u = (hc)/(\lambda)


\lambda = (6.626 * 10^(-34) * 3 * 10^(8))/(7.2 * 10^(-19))

=
(6.626 * 3 * 10^(-26))/(7.2 * 10^(-19))

=
2.76 * 10^(-7) m

Hence, the wavelength of the ejected electrons is
2.76 * 10^(-7) m.

(c) For iron surface,
\phi = 4.7 eV

=
(4.7 * 1.6 * 10^(-19)) J

=
7.52 * 10^(-19) J

Here, the value of
\phi is more than the value of UV light source. Hence, we need a shorter wavelength light as we know that,


E \propto (1)/(\lambda)

Therefore, lesser will be the wavelength higher will be the energy.

User Theplau
by
8.5k points
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