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![1) In a band structure calculation, the dispersion relation for
electrons is found to be
𝜺 𝑲=𝜷(𝒄𝒐𝒔𝒌 𝒙a+cos𝒌 𝒚a+cos𝒌 𝒛a)
where β is a constant and a is the lattice constant. The
effective mass at the boundary of the first Brillouin zone is
[NET/JRF -DEC 2012]
(a)
𝟐ℏ 𝟐
𝟓𝜷𝒂 𝟐
(b)
𝟒ℏ 𝟐
𝟓𝜷𝒂 𝟐
(c)
ℏ 𝟐
𝟐𝜷𝒂 𝟐
(d)
ℏ 𝟐
𝟑𝜷𝒂 𝟐
Ans : (d)](https://image.slidesharecdn.com/srininet-190909090302/85/Srini-net-2-320.jpg)
![2)The radius of the Fermi sphere of free electrons in a
monovalent metal with an fcc structure, in which the
volume of the unit cell is 𝒂 𝟑
, is
[NET/JRF -DEC 2012]
(a)𝝅 𝟐
(b)
𝟑𝝅 𝟐
𝒂
𝟐
𝟑
(c)
𝟏𝟐𝝅 𝟐
𝒂 𝟑
𝟏
𝟑
(d)
𝝅
𝒂 𝟐
𝟓
𝟑
Ans : (c)](https://image.slidesharecdn.com/srininet-190909090302/85/Srini-net-3-320.jpg)
![3) The pressure of a nonrelativistic free Fermi gas in
three-dimensions depends, at T=0 , on the density of
fermions n as
[ NET/JRF (JUNE-2014)]
(a) n
(b) 𝒏 𝟐
(c) 𝒏
𝟒
𝟑
(d) 𝒏
𝟓
𝟑
Ans : (d)](https://image.slidesharecdn.com/srininet-190909090302/85/Srini-net-4-320.jpg)
![4) The dispersion relation of electrons in a 3-dimensional lattice in the tight
binding approximation is given by,
𝜺 𝑲=𝜶𝒄𝒐𝒔𝒌 𝒙a+𝜷cos𝒌 𝒚a+𝜸cos𝒌 𝒛a
where a is the lattice constant and α, β ,γ are constants with dimension of
energy. The effective mass tensor at the corner of the first Brillouin zone
𝝅
𝒂
,
𝝅
𝒂
,
𝝅
𝒂
is [ NET/JRF (JUNE-2015)]
(a)
ℏ 𝟐
𝒂 𝟐
−𝟏
𝜶
𝟎 𝟎
𝟎
−𝟏
𝜷
𝟎
𝟎 𝟎
−𝟏
𝜸
(b)
ℏ 𝟐
𝒂 𝟐
−𝟏
𝜶
𝟎 𝟎
𝟎
𝟏
𝜷
𝟎
𝟎 𝟎
−𝟏
𝜸
(c )
ℏ 𝟐
𝒂 𝟐
𝟏
𝜶
𝟎 𝟎
𝟎
𝟏
𝜷
𝟎
𝟎 𝟎
𝟏
𝜸
(d )
ℏ 𝟐
𝒂 𝟐
𝟏
𝜶
𝟎 𝟎
𝟎
𝟏
𝜷
𝟎
𝟎 𝟎
−𝟏
𝜸
Ans : (c)](https://image.slidesharecdn.com/srininet-190909090302/85/Srini-net-5-320.jpg)
![5) If the number density of a free electron gas in three
dimensions is increased eight times, its Fermi
temperature will
[ NET/JRF (JUNE-2011)]
(a) increase by a factor of 4
(b) decrease by a factor of 4
(c) increase by a factor of 8
(d) decrease by a factor of 8
Ans : (a)](https://image.slidesharecdn.com/srininet-190909090302/85/Srini-net-6-320.jpg)
Srini net
- 1.
- 2. 1) In aband structure calculation, the dispersion relation for electrons is found to be 𝜺 𝑲=𝜷(𝒄𝒐𝒔𝒌 𝒙a+cos𝒌 𝒚a+cos𝒌 𝒛a) where β is a constant and a is the lattice constant. The effective mass at the boundary of the first Brillouin zone is [NET/JRF -DEC 2012] (a) 𝟐ℏ 𝟐 𝟓𝜷𝒂 𝟐 (b) 𝟒ℏ 𝟐 𝟓𝜷𝒂 𝟐 (c) ℏ 𝟐 𝟐𝜷𝒂 𝟐 (d) ℏ 𝟐 𝟑𝜷𝒂 𝟐 Ans : (d)
- 3. 2)The radius ofthe Fermi sphere of free electrons in a monovalent metal with an fcc structure, in which the volume of the unit cell is 𝒂 𝟑 , is [NET/JRF -DEC 2012] (a)𝝅 𝟐 (b) 𝟑𝝅 𝟐 𝒂 𝟐 𝟑 (c) 𝟏𝟐𝝅 𝟐 𝒂 𝟑 𝟏 𝟑 (d) 𝝅 𝒂 𝟐 𝟓 𝟑 Ans : (c)
- 4. 3) The pressureof a nonrelativistic free Fermi gas in three-dimensions depends, at T=0 , on the density of fermions n as [ NET/JRF (JUNE-2014)] (a) n (b) 𝒏 𝟐 (c) 𝒏 𝟒 𝟑 (d) 𝒏 𝟓 𝟑 Ans : (d)
- 5. 4) The dispersionrelation of electrons in a 3-dimensional lattice in the tight binding approximation is given by, 𝜺 𝑲=𝜶𝒄𝒐𝒔𝒌 𝒙a+𝜷cos𝒌 𝒚a+𝜸cos𝒌 𝒛a where a is the lattice constant and α, β ,γ are constants with dimension of energy. The effective mass tensor at the corner of the first Brillouin zone 𝝅 𝒂 , 𝝅 𝒂 , 𝝅 𝒂 is [ NET/JRF (JUNE-2015)] (a) ℏ 𝟐 𝒂 𝟐 −𝟏 𝜶 𝟎 𝟎 𝟎 −𝟏 𝜷 𝟎 𝟎 𝟎 −𝟏 𝜸 (b) ℏ 𝟐 𝒂 𝟐 −𝟏 𝜶 𝟎 𝟎 𝟎 𝟏 𝜷 𝟎 𝟎 𝟎 −𝟏 𝜸 (c ) ℏ 𝟐 𝒂 𝟐 𝟏 𝜶 𝟎 𝟎 𝟎 𝟏 𝜷 𝟎 𝟎 𝟎 𝟏 𝜸 (d ) ℏ 𝟐 𝒂 𝟐 𝟏 𝜶 𝟎 𝟎 𝟎 𝟏 𝜷 𝟎 𝟎 𝟎 −𝟏 𝜸 Ans : (c)
- 6. 5) If thenumber density of a free electron gas in three dimensions is increased eight times, its Fermi temperature will [ NET/JRF (JUNE-2011)] (a) increase by a factor of 4 (b) decrease by a factor of 4 (c) increase by a factor of 8 (d) decrease by a factor of 8 Ans : (a)
- 7.