Question

2: The Fermi energy in silver is 5.51 eV. (A) What is the average energy of the free electrons in silver at 0 K? (b) What temperature is necessary for the average molecular energy in an ideal gas to have this value? (c) What is the speed of an electron with this

Answer 1

Answer:

Given data:

E(F) = 5.51 ev

To find:

Average energy of free e- in silver = ?

The formula to find the number of free electrons in silver is.

E = 3/5 E(F)

E = 5/3 x 5.51

E = 3.306 eV

Hence the average energy of the free electrons in silver at 0 k is  3.306 eV.

Explanation:

follow me plz

Answer 2

Answer:

(A) 3.306ev.

(B) T=2.55×10⁴ K

(C) 1.078×$10^{6}$ m/s

Explanation:

E(F)= 5.51 eV

Part A:

Formula for calculating average energy of free electrons at 0K,

$Average Energy=\frac{3}{5} E(F)$

$Average Energy=\frac{3}{5} *5.51$

=3.306ev.

Part B:

Formula for average molecular energy in an ideal gas in terms of temperature,

$\frac{3}{2}KT=Averge Energy\\ T=\frac{2* Averge energy}{3K} \\T=\frac{2*3.306eV}{3K}\\ T=\frac{2*5.289*10^{-19} }{3*1.38*10^{-23} }$

On solving,

T=2.55×10⁴ K

Part C:

Formula for Speed of the electron at 0K (Fermi Energy)

Speed=V(F)=$\sqrt{\frac{2*Average Energy}{3} }$

$V(F)=\sqrt{\frac{2*5.289*10^{-19} }{9.1*10^{-31} } }\\ V(F)=1.078*10^{6}m/s$

Speed of electron=1.078×$10^{6}$ m/s