Winter 2016 - Q.6 - Grad Plus

# Winter 2016 – Q.6

6. (a) The electron which is at rest is accelerated through a potential difference of 200V. Calculate
i) The velocity of electron
ii) De-Brouglie wavelength
iii) Momentum. [5M]

We have,
i. velocity of electron,

$latex \begin{array}{l}\nu=\sqrt{\frac{2eV}m}\\\\\;\;\;=\sqrt{\frac{2\times1.6\times10^{-19}\times200}{9.1\times10^{-31}}}\\\\\;\;\;=8.38\times10^{-6}m/s\end{array}$

ii. de-Broglie wavelength of electron,

$latex \begin{array}{l}\lambda=\frac h{m\nu}\\\\\;\;\;=\frac{6.63\times10^{-34}}{9.1\times10^{-31}\times8.38\times10^6}\\\\\;\;\;=0.0869\times10^{-9}m\\\\\;\;\;=0.00869\;\overset\circ A\end{array}$

iii) Momentum,

$latex \begin{array}{l}p=mv\\\\=9.1\times10^{-31}\times8.38\times10^6\\\\=76.258\times10^{-25}kgm/s^2\end{array}$

(b) Explain how Lissajous figures are used in determine the phase difference between two A.C. signals. [5M]

When two sine waves oscillating in mutually perpendicular direction are of same frequency, the Lissajous pattern takes the form of an ellipse as shown in the figure. This ellipse is used to determine the phase difference between two signals, by using the formula

$latex \phi=\sin^{-1}\left(\frac{AA’}{BB’}\right)$

The two sinusoidal voltages having same amplitude and frequency but having phase difference Φ, is applied to X and Y-inputs of CRO. A proper voltage sensitivity and time sensitivity is selected so as to obtain two or three cycles of AC. Then by combining the two signals ellipse is obtained on the CRO screen. By measuring the length AA’ and BB’ on the oscillogram as shown in the figure and substituting the values in the above formula phase difference can be determined.

(c) What are nano materials? Explain any two methods for synthesis of Nanoparticles. [5M]

Nanomaterials are materials which are characterized by an ultra fine grain size (< 50 nm) or by a
dimensionality limited to 50 nm. Nanomaterials have extremely small size which having at least one dimension 100 nm or less. Nanomaterials can be nanoscale in one dimension (eg. surface films), two dimensions (eg. strands or fibres), or three dimensions (eg. particles). They can exist in single, fused, aggregated or agglomerated forms with spherical, tubular, and irregular shapes. Common types of nanomaterials include nanotubes, dendrimers, quantum dots and fullerenes.

Synthesis of Nanomaterial
Mechanical milling: In this synthesis method coarse-grained material (metals, ceramics or polymers) in the form of powders are crushed mechanically in rotating drums by hard steel or tungsten carbide balls, usually under controlled atmospheric conditions to prevent unwanted reactions such as oxidation. This repeated deformation can cause large reductions in grain size via the formation and organization of grain boundaries within the powder particles. Different components can be mechanically alloyed together by cold welding to produce nanostructured alloys. A nanometer dispersion of one phase in another can also be achieved.

Hydrothermal Technique: Hydrothermal synthesis can be defined as a method of synthesizing single crystals which depends on the solubility of minerals in hot water under high pressure. In short, the synthesis method uses the solubility in water of almost all inorganic substances at elevated temperatures and pressures, and subsequent crystallization of the dissolved material from fluid.

Crystal growth is performed in an apparatus consisting of a steel pressure vessel called an autoclave, which contains thick-walled steel cylinders with a hermetic seal which can withstand high temperatures and pressures for prolonged periods of time. Furthermore, the autoclave material is inert with respect to the solvent.

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