Question

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.

Answer 1

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.