Find the maximum wavelength of electromagnetic radiation
Question: Find the maximum wavelength of electromagnetic radiation which can create a hole-electron pair in germanium. The band gap in germanium is $0.65 \mathrm{eV}$. Solution:...
Read More →Suppose the energy liberated in the recombination of
Question: Suppose the energy liberated in the recombination of a ahole-electron pair is converted iinto electromagnetic radiation. If the maximum wavelength emitted is $820 \mathrm{~nm}$, what is the band gap? Solution:...
Read More →The band gap between the valence and the conduction bands
Question: The band gap between the valence and the conduction bands in zinc oxide (ZnO) is $3.2 \mathrm{eV}$. Suppose an electron in the conduction band combines with a hole in the valence band the excess energy is released in the form of electromagnetic radiation. Find the maximum wavelength that can be emitted in this process. Solution:...
Read More →When a semiconducting material is doped with an impurity.
Question: When a semiconducting material is doped with an impurity. New acceptor levels are created. In a particular thermal collision, a valence electron receives an energy equal to $2 \mathrm{kT}$ and just reaches one of the acceptor levels. Assuming that the energy of the energy of the electron was at the top edge of the valence band and that the temperature $T$ is equal to $300 \mathrm{k}$, find the energy of the acceptor levels above the valence band. Solution:...
Read More →Solve this following
Question: Evaluate: i. $\int(2-5 x)(3+2 x)(1-x) d x$ ii. $\int \sqrt{x}\left(a x^{2}+b x+c\right) d x$ iii. $\int\left(\sqrt{x}-\sqrt[3]{x^{4}}+\frac{7}{\sqrt[3]{x^{2}}}-6 x^{x}+1\right) d x$ Solution:...
Read More →The band gap for silicon is 1.1eV. (a) Find the ratio of the band gap to kT for silicon at room temperature 300k.
Question: The band gap for silicon is $1.1 \mathrm{eV}$. (a) Find the ratio of the band gap to $\mathrm{kT}$ for silicon at room temperature $300 \mathrm{k}$. (b) At what temperature does this ratio become one tenth of the value at $300 \mathrm{k}$ ? (Silicon will not retain its structure at these high temperatures.) Solution:...
Read More →Indium antimonide has a band gap of 0.23eV
Question: Indium antimonide has a band gap of $0.23 \mathrm{eV}$ between the valence and the conduction band. Find the temoerture at which $\mathrm{kT}$ equals the band gap. Solution: ABC...
Read More →Solve this following
Question: Evaluate: i. $\int\left(6 x^{5}-\frac{2}{x^{4}}-7 x+\frac{3}{x}-5+4 e^{x}+7^{x}\right) d x$ ii. $\int\left(8-x+2 x^{3}-\frac{6}{x^{3}}+2 x^{-5}+5 x^{-1}\right) d x$ iii. $\int\left(\frac{x}{a}+\frac{a}{x}+x^{a}+a^{x}+a x\right) d x$ Solution:...
Read More →In a pure semiconductor, the number of conduction electrons is
Question: In a pure semiconductor, the number of conduction electrons is $6 \times 10^{19} \mathrm{Per}$ cubic mertre. How many holes are there in a sample of size $1 \mathrm{~cm} \times 1 \mathrm{~cm} \times 1 \mathrm{~cm}$ ? Solution:...
Read More →Calculate the number of states per cubic meter of sodium in
Question: Calculate the number of states per cubic meter of sodium in $3 \mathrm{~s}$ band. The density of sodium is $1013 \mathrm{~kg} / \mathrm{cm}^{3}$, How many of them are empty? Solution:...
Read More →Solve this following
Question: Evaluate: i. $\int x^{7} d x$ ii. $\int x^{-7} d x$ iii. $\int x^{-1} d x$ iv. $\int x^{5 / 3} d x$ v. $\int x^{-5 / 4} d x$ vi. $\int 2^{x} d x$ vii. $\int \sqrt[3]{\mathrm{x}^{2}} \mathrm{dx}$ viii. $\int \frac{1}{\sqrt[4]{x^{3}}} d x$ ix. $\int \frac{2}{x^{2}} d x$ Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in the following: The least value of $f(x)=\left(e^{x}+e^{-x}\right)$ is A. $-2$ B. 0 C. 2 D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in the following: The maximum value of $f(x)=(x-2)(x-3)^{2}$ is A. $\frac{7}{3}$ B. 3 C. $\frac{4}{27}$ D. 0 Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in the following: The minimum value of $f(x)=3 x^{4}-8 x^{3}-48 x+25$ on $[0,3]$ is A. 16 B. 25 C. $-39$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in the following: The minimum value of $\left(\mathrm{x}^{2}+\frac{250}{\mathrm{x}}\right)$ is A. 0 B. 25 C. 50 D. 75 Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in the following: If $x0$ and $x y=1$, the minimum value of $(x+y)$ is A. $-2$ B. 1 C. 2 D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in the following: $f(\mathrm{x})=\operatorname{cosec} \mathrm{x}$ in $(-\pi, 0)$ has a maxima at A. $x=0$ B. $x=\frac{-\pi}{4}$ C. $x=\frac{-\pi}{3}$ D. $\mathrm{x}=\frac{-\pi}{2}$ Solution:...
Read More →Consider an excited hydrogen atom in state n moving with
Question: Consider an excited hydrogen atom in state $n$ moving with a velocity $v(vc)$. It emits a photon in the direction of its motion and changes its state to a lower state m. Apply momentum and energy conservation principles to calculate the frequency $v$ of the emitted radiation. Compare this with the frequency $v_{0}$ emitted if the atom were at rest. Solution:...
Read More →longest possible wavelength emitted by hydrogen atoms in visible
Question: longest possible wavelength emitted by hydrogen atoms in visible range in such a world according to Bohr's model? Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in the following: The maximum value of $\left(\frac{\log x}{x}\right)$ is A. $\left(\frac{1}{e}\right)$ B. $\frac{2}{\mathrm{e}}$ C. e D. 1 Solution:...
Read More →A uniform magnetic field B exists in a region.
Question: A uniform magnetic field B exists in a region. An electron projected perpendicular to the field goes in a circle. Assuming Bohr's quantization rule for angular momentum, calculate The smallest possible radius of the electron The radius of the ${ }^{\text {nth }}$ orbit and The minimum possible speed of the electron. Solution:...
Read More →Consider a neutron and an electron bound to each other due to gravitational force.
Question: Consider a neutron and an electron bound to each other due to gravitational force. Assuming Bohr's quantization rule for angular momentum to be valid in this case' derive an expression for the energy of the neutron-electron system. Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in the following: When $x$ is positive, the minimum value of $\mathrm{X}^{\mathrm{x}}$ is A. $e^{e}$ B. $e^{1 / e}$ C. $e^{-1 / e}$ D. $(1 / \mathrm{e})$ Solution: Hence, $C$ is the correct answer....
Read More →The earth resolves round the sun due to gravitational attraction.
Question: The earth resolves round the sun due to gravitational attraction. Suppose that the sun and the earth are point particles with their existing masses and that Bohr's quantization rule for angular momentum is valid in the case of gravitation. Calculate the minimum radius the earth can have for its orbit. What is the value of the principal quantum number $n$ for the present radius? Mass of the earth $=6.0 \times 10^{24} \mathrm{~kg}$, mass of the sun $=2.0 \times 10^{20}$, earth - sun dist...
Read More →A filter transmits only the radiation of wavelength greater than
Question: A filter transmits only the radiation of wavelength greater than $440 \mathrm{~nm}$. Radiation from a hydrogen discharge tube goes through such a filter and is incident on a metal of work function $2.0 \mathrm{eV}$. Find the stopping potential which can stop the photoelectrons. Solution:...
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