Problem set 96

1. The transient response of an electronic circuit is tested by giving the following wave form at the input:
1. Sinusoidal
2. Square
3. Triangular
4. Saw-tooth

Square

Hence, answer is (B)

2. Which of the following effects manifests particle nature of light?
1. Photo electric effect
2. Blackbody radiation
3. Interference
4. Diffraction

Photo electric effect

Hence, answer is (A)

3. A ruled grating having 1000 grooves per mm is used for diffraction. If light of wavelength 300 nm is incident at right angle and if $\theta$ is the diffraction angle, $\sin\theta$ for first order diffraction will be equal to:
1. 0.1
2. 0.3
3. 0.2
4. 0.5

Using relation $d\sin\theta=n\lambda$, where $d=\frac{1\times10^6}{1000}nm=10^3 nm$ and $n=1$

$\sin\theta=\frac{300}{10^3}=0.3$

Hence, answer is (B)

4. The conventional unit cell of a body-centered cubic Bravais lattice is shown in the figure above. The conventional cell has volume $a^3$. What is the volume of the primitive unit cell?
1. $\frac{a^3}{8}$
2. $\frac{a^3}{4}$
3. $\frac{a^3}{2}$
4. $a^3$
The primitive vectors of BCC structure are $$\bar a_1=a\hat x$$ $$\bar a_2=a\hat y$$ $$\bar a_3=\frac{a}{2}\left(\hat x+\hat y+\hat z\right)$$ Hence, volume of primitive cell is $\frac{a^3}{2}$

Hence, answer is (C)

5. If the absolute temperature of a blackbody is increased by a factor of 3, the energy radiated per second per unit area does which of the following
1. Decreases by a factor of 81.
2. Decreases by a factor of 9.
3. Increases by a factor of 9.
4. Increases by a factor of 81.

According to Stefan's Law the radiated power density(W/m2) of a black body is proportional to fourth power of its absolute temperature $$E=e\sigma T^4$$ The emissivity $e=1-R$ is a correction for an approximate black body radiator, where $R$ is the fraction of the light reflected. For perfectly black body $R=0$ $$\frac{E}{E'}=\frac{T^4}{T'^4}$$

Hence, answer is (D)