Question

PAGE: calculate the energy gap of Si, given that radiation of
wavelength 11,000 amstrong is incident on it. also find
allowed wavelength for Ge with energy gap
0.90 ev.

Answer 1

The energy band gap of silicon is – 1.12 eV.

The allowed wavelength for Ge is – 13790 A°.

Given: a) Radiation of wavelength 11,000 A° is incident on Si.

           b) Energy gap of Ge is 0.90eV.

To find: a) Energy gap of silicon.

             b) Allowed wavelength for Ge.

Solution:

The wavelength of light that is reflected by a solid and its energy band gap are related to one another by the Planck-Einstein Relation, which is given by,

E = hc/λ

where E is the energy gap.

h is planck's constant h = 6.62 * 10⁻³⁴ Joule-seconds.

c is the speed of light. c = 3 * 10⁸ m/s.

λ is the wavelength in metres.

a) We are given λ = 11000 Α°

        or λ = 11000 * 10⁻¹⁰ m        Using 1 Α° = 10⁻¹⁰ m    

Now, using the Planck-Einstein Relation,

E = hc/λ

E =  (6.62 *  10⁻³⁴ * 3 * 10⁸ ) / 11000 * 10⁻¹⁰

E = (6.62 * 3 )/11 * 10⁻¹⁹ Joules

E = 1.805 * 10⁻¹⁹ Joules

To find Energy in electron-volt or eV,

1 eV = 1.6 x 10⁻¹⁹ Joules.

or 1 Joule = 0.625 * 10¹⁹ eV.

E = 1.805 * 0.625 * 10⁻¹⁹ * 10¹⁹ eV

E = 1.12 eV

Hence, energy gap of Silicon is 1.12 eV.

b) We are given energy gap of Ge = 0.90 eV.

Using Planck-Einstein Relation,

E = hc/λ

λ = hc/E

E = 0.90 eV or

E = 0.90 * 1.6 x 10⁻¹⁹ Joules

E = 1.44 * 10⁻¹⁹ Joules

λ = (6.62 *  10⁻³⁴ * 3 * 10⁸ ) / ( 1.44 * 10⁻¹⁹ ) in metres

λ = 13.79 * 10 ⁻⁷ m

λ = 13.79 * 10 ⁻⁷ * 10¹⁰ A°

λ = 13.79 * 1000 A°

λ= 13790 A°

Hence, allowed wavelength for Ge with energy gap 0.90 eV is  13790 A°.

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