A particle moves in a closed orbit around the origin,
Question: A particle moves in a closed orbit around the origin, due to a force which is directed towards the origin. The de Broglie wavelength of the particle varies cyclically between two values 1, 2 with 12. Which of the following statement are true? (a) The particle could be moving in a circular orbit with origin as centre (b) The particle could be moving in an elliptic orbit with origin as its focus (c) When the de Broglie wavelength is 1, the particle is nearer the origin than when its valu...
Read More →Photons absorbed in matter are converted to heat.
Question: Photons absorbed in matter are converted to heat. A source emitting n photon/sec of frequency is used to convert 1kg of ice at 0C to water at 0C. Then, the time T taken for the conversion (a) decreases with increasing n, with fixed (b) decreases with n fixed, increasing (c) remains constant with n and changing such that n = constant (d) increases when the product n increases Solution: The correct answers are (a) decreases with increasing n, with fixed (b) decreases with n fixed, increa...
Read More →An urn contains 9 red, 7 white, and 4 black balls.
Question: An urn contains 9 red, 7 white, and 4 black balls. A ball is drawn at random. Find the probability that the ball is drawn is not white Solution: We know that, Probability of occurrence of an event $=\frac{\text { Total no.of Desired outcomes }}{\text { Total no.of outcomes }}$ By permutation and combination, total no. of ways to pick r objects from given $n$ objects is ${ }^{n} C_{r}$ Now, total no.of ways to pick a ball from 20 balls is ${ }^{20} \mathrm{C} 1=20$ Our desired output is...
Read More →The de Broglie wavelength of a photon
Question: The de Broglie wavelength of a photon is twice the de Broglie wavelength of an electron. The speed of the electron is ve= c/100. Then (a) Ee/Ep = 10-4 (b) Ee/Ep = 10-2 (c) Pe/mec = 10-2 (d) Pe/mec = 10-4 Solution: The correct answers are (b) Ee/Ep = 10-2 (c) Pe/mec = 10-2...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{x^{2}}{x^{2}+7 x+10} d x$ Solution: Given $I=\int \frac{x^{2}}{x^{2}+7 x+10} d x$ Expressing the integral $\int \frac{\mathrm{P}(\mathrm{x})}{\mathrm{ax}^{2}+\mathrm{bx}+\mathrm{c}} \mathrm{dx}=\int \mathrm{Q}(\mathrm{x}) \mathrm{dx}+\int \frac{\mathrm{R}(\mathrm{x})}{\mathrm{ax}^{2}+\mathrm{bx}+\mathrm{c}} \mathrm{dx}$ $\Rightarrow \int \frac{x^{2}}{x^{2}+7 x+10} d x=\int\left(\frac{-7 x-10}{x^{2}+7 x+10}+1\right) d x$ $=-\int \frac{7 x+10...
Read More →Two particles A1 and A2 of masses m1,
Question: Two particles A1 and A2 of masses m1, m2 (m1 m2) have the same de Broglie wavelength. Then (a) their momenta are the same (b) their energies are the same (c) energy of A1 is less than the energy of A2 (d) energy of A1 is more than the energy of A2 Solution: The correct answers are (a) their momenta are the same (c) energy of A1 is less than the energy of A2...
Read More →Relativistic corrections become necessary
Question: Relativistic corrections become necessary when the expression for the kinetic energy 1/2 mv2 , becomes comparable with mc2, where m is the mass of the particle. At what de Broglie wavelength will relativistic corrections become important for an electron? (a) =10nm (b) =101nm (c) =104nm (d) =106nm Solution: The correct answers are (c) =104nm (d) =106nm...
Read More →An urn contains 9 red, 7 white, and 4 black balls.
Question: An urn contains 9 red, 7 white, and 4 black balls. A ball is drawn at random. Find the probability that the ball is drawn is white or black Solution: We know that, Probability of occurrence of an event $=\frac{\text { Total no. of Desired outcomes }}{\text { Total no.of outcomes }}$ By permutation and combination, total no. of ways to pick r objects from given $n$ objects is ${ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}$ Now, total no. of ways to pick a ball from 20 balls is ${ }^{20} \mat...
Read More →An electron (mass m) with an initial velocity
Question: An electron (mass m) with an initial velocityis in an electric field. If 0= h/mv0, its de Broglie wavelength at time t is given by (a) 0 (b) $\lambda_{0} \sqrt{1+\frac{e^{2} E_{0}^{2} t^{2}}{m^{2} v_{0}^{2}}}$ (c) $\frac{\lambda_{0}}{\sqrt{1+\frac{e^{2} E_{0}^{2} t^{2}}{m^{2} v_{0}^{2}}}}$ (d) $\frac{\lambda_{0}}{1+\frac{e^{2} E_{0}^{2} t^{2}}{m^{2} v_{0}^{2}}}$ Solution: The correct answer is c) $\frac{\lambda_{0}}{\sqrt{1+\frac{e^{2} E_{0}^{2} t^{2}}{m^{2} v_{0}^{2}}}}$...
Read More →An electron (mass m ) with an initial velocity
Question: An electron (mass m ) with an initial velocityis in an electric fieldIts de Broglie wavelength at time t is given by (a) $\frac{\lambda_{0}}{1+\frac{e E_{0}}{m} \frac{t}{v_{0}}}$ (b) $\lambda_{0}\left(1+\frac{e E_{0} t}{m v_{0}}\right)$ (c) 0 (d) 0t Solution: The correct answer is (a) $\frac{\lambda_{0}}{1+\frac{e E_{0}}{m} \frac{t}{v_{0}}}$...
Read More →An urn contains 9 red, 7 white, and 4 black balls.
Question: An urn contains 9 red, 7 white, and 4 black balls. A ball is drawn at random. Find the probability that the ball is drawn is red or white Solution: We know that, Probability of occurrence of an event $=\frac{\text { Total no.of Desired outcomes }}{\text { Total no.of outcomes }}$ By permutation and combination, total no.of ways to pick $r$ objects from given $n$ objects is ${ }^{n} \mathrm{C}_{r}$ Now, total no.of ways to pick a ball from 20 balls is ${ }^{20} \mathrm{C}_{1}=20$ Our de...
Read More →An urn contains 9 red, 7 white, and 4 black balls.
Question: An urn contains 9 red, 7 white, and 4 black balls. A ball is drawn at random. Find the probability that the ball is drawn is white Solution: We know that, Probability of occurrence of an event $=\frac{\text { Total no.of Desired outcomes }}{\text { Total no.of outcomes }}$ By permutation and combination, total no.of ways to pick $\mathrm{r}$ objects from given $\mathrm{n}$ objects is ${ }^{n} C_{r}$ Now, total no. of ways to pick a ball from 20 balls is ${ }^{20} \mathrm{C}_{1}=20$ Our...
Read More →An electron is moving with an initial velocity
Question: An electron is moving with an initial velocityand is in a magnetic fieldThen its de Broglie wavelength (a) remains constant (b) increases with time (c) decreases with time (d) increases and decreases periodically Solution: The correct answer is (a) remains constant...
Read More →An urn contains 9 red, 7 white, and 4 black balls.
Question: An urn contains 9 red, 7 white, and 4 black balls. A ball is drawn at random. Find the probability that the ball is drawn is red Solution: We know that Probability of occurrence of an event $=\frac{\text { Total no.of Desired outcomes }}{\text { Total no.of outcomes }}$ By permutation and combination, total no.of ways to pick $r$ objects from given $n$ objects is ${ }^{n} C_{r}$ Now, total no.of ways to pick a ball from 20 balls is ${ }^{20} \mathrm{C}_{1}=20$ Our desired output is to ...
Read More →A proton, a neutron,
Question: A proton, a neutron, an electron and an -particle have the same energy. Then their de Broglie wavelengths compare as (a) p = n e (b) p = n e (c) e p = n (d) e = p = n = Solution: The correct answer is (b) p = n e...
Read More →Evaluate the following integrals:
Question: $\int \frac{x^{2}+1}{x^{2}-5 x+6} d x$ Solution: Consider $I=\int \frac{x^{2}+1}{x^{2}-5 x+6} d x$ Expressing the integral $\int \frac{\mathrm{P}(\mathrm{x})}{\mathrm{ax}^{2}+\mathrm{bx}+\mathrm{c}} \mathrm{dx}=\int \mathrm{Q}(\mathrm{x}) \mathrm{dx}+\int \frac{\mathrm{R}(\mathrm{x})}{\mathrm{ax}^{2}+\mathrm{bx}+\mathrm{c}} \mathrm{dx}$ $\Rightarrow \int \frac{x^{2}+1}{x^{2}-5 x+6} d x=\int\left(\frac{5 x-5}{x^{2}-5 x+6}+1\right) d x$ $=5 \int \frac{x-1}{x^{2}-5 x+6} d x+\int 1 d x$ Co...
Read More →Suppose the voltage applied to A is increased.
Question: Suppose the voltage applied to A is increased. The diffracted beam will have the maximum at a value of that (a) will be larger than the earlier value (b) will be the same as the earlier value (c) will be less than the earlier value (d) will depend on the target Solution: The correct answer is (c) will be less than the earlier value...
Read More →A bag contains 4 white and 5 black balls.
Question: A bag contains 4 white and 5 black balls. A ball is drawn at random from the bag. Find the probability that the ball is drawn is white. Solution: We know that, Probability of occurrence of an event $=\frac{\text { Total no.of Desired outcomes }}{\text { Total no.of outcomes }}$ By permutation and combination, total no.of ways to pick r objects from given n objects is ${ }^{n} C_{r}$ Now, total no. of ways to pick a ball from 9 balls is ${ }^{9} \mathrm{C}_{1}=9$ Our desired output is t...
Read More →Consider a beam of electrons (each electron with energy E0)
Question: Consider a beam of electrons (each electron with energy E0) incident on a metal surface kept in an evacuated chamber. Then (a) no electrons will be emitted as only photons can emit electrons (b) electrons can be emitted but all with an energy, E0 (c) electrons can be emitted with any energy, with a maximum of E0 ( is the work function) (d) electrons can be emitted with any energy, with a maximum of E0 Solution: The correct answer is (d) electrons can be emitted with any energy, with a ...
Read More →The wavelength of a photon needed to remove
Question: The wavelength of a photon needed to remove a proton from a nucleus which is bound to the nucleus with 1 MeV energy is nearly (a) 1.2 nm (b) 1.2 103nm (c) 1.2 106nm (d) 1.2 101nm Solution: The correct answer is (b) 1.2 103nm...
Read More →A particle is dropped from a height H.
Question: A particle is dropped from a height H. The de Broglie wavelength of the particle as a function of height is proportional to (a) H (b) H (c) H0 (d) H1/2 Solution: The correct answer is (d) H1/2...
Read More →In a single throw of two dice, find
Question: In a single throw of two dice, find P (a total of 9 or 11) Solution: We know that, Probability of occurrence of an event $=\frac{\text { Total no.of Desired outcomes }}{\text { Total no.of outcomes }}$ Total outcomes are $(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)$, $(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)$, $(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)$, $(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)$, $(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)$, $(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)$ Desired outcomes are $(3,6),(4,5),(5...
Read More →In a single throw of two dice, find
Question: In a single throw of two dice, find P (a total greater than 8) Solution: We know that, Probability of occurrence of an event $=\frac{\text { Total no. of Desired outcomes }}{\text { Total no. of outcomes }}$ Total outcomes are $(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)$, $(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)$, $(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)$, $(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)$, $(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)$, $(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)$ Desired outcomes are $(3,6),(4...
Read More →To ensure almost 100 per cent transmissivity,
Question: To ensure almost 100 per cent transmissivity, photographic lenses are often coated with a thin layer of dielectric material. The refractive index of this material is intermediated between that of air and glass (which makes the optical element of the lens). A typically used dielectric film is MgF2 (n = 1.38). What should the thickness of the film be so that at the centre of the visible spectrum (5500 Ao) there is maximum transmission? Solution: IA is incident at point A such that there ...
Read More →The optical properties of a medium are governed
Question: The optical properties of a medium are governed by the relative permittivity (r) and relative permeability (r ). The refractive index is defined as r r = n. For ordinary material r 0 and r 0 and the positive sign is taken for the square root. In 1964, a Russian scientist V. Veselago postulated the existence of material with r 0 and r 0. Since then such metamaterials have been produced in the laboratories and their optical properties studied. For such materials n = -rr. As light enters ...
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