Question

The work needed to remove an electron from the surface of rutile TiO2 is 3.0 eV. What is the longest wavelength at which we can have free electrons within the material and outside of it? What will be the stopping potential for electrons if TiO2 is irradiated with light with wavelength of 200 nm? What will the stopping potential be if TiO2 is irradiated with 530 nm wavelength? What is the photoelectron energy ratio for aforementioned wavelengths?

Answer 1

1.

The work needed to remove an electron from the metal surface is the work function . The work function is given by ,

0 = 3 eV

hc / = 3 eV

= ( hc)/ 3 eV

= ( 6.626 × 10 -34  × 3 × 10 8 ) /( 3× 1.6 × 10 -19 )

= 4.14 × 10 -7 m.

2.

​​1 = 200nm

Energy E = hc /

E 1 = hc 1

E 1 = (6.626 × 10 -34 × 3 × 10 8 ) / (200 × 10 -9)

E 1 = 9.939 × 10 -19 v

E 1 = 6.21 eV

Stopping potential V​​​​​​ 0 = ( E 1 - 0)

V 0 = 6.21 eV - 3 eV

V 0 = 3.21 eV

Stopping potential for wavelength 200nm is 3.21 eV

3.

2 = 530 nm

Energy E = hc /

E 2 = hc / 2

E 2 = (6.626 × 10 -34 × 3 × 108 ) / (530 × 10-9)

E 2 = 3.75 × 10 -19 V

E 2 = 2.344 eV

Stopping potential V 0 = ( 2.344 eV - 3 eV)

V 0 = - 0.656 eV

Stopping potential for wavelength 530 nm is - 0.656 eV

4. Energy ratio for the above wavelength 200nm and 530nm

E 1 / E 2  = (6.21 eV / 2.344 eV )

E 1 / E 2 = 2.65

The photoelectron energy ratio for the wavelength 200nm and 530 nm is 2.65