29 + Interview Questions in WAVE-PARTICLE-DUALITY IN GENERAL AWARENESS Page 1 InterviewSolution

1.	A microwave oven operates at `2.5` GHz. Assume that `5%` of microwave photons are absorbed by 200 ml of water kept inside the oven. The time needed to warm the water from `20^(@)C `to `70^(@)C` is 2 minute. Specific heat capacity of water is `4.2 Jg^(–1) .^(@)C^(–1)`. Neglect any heat loss by water to the surrounding. Calculate the number of photons emitted per second per kilowatt of power consumed by the microwave. Efficiency of the oven to convent electrical energy into microwave energy is `70%`
Answer» Correct Answer - `4.22 xx 10^(26)`

Discussion

2.	When photons of wavelength `lambda_(1) = 2920 Å` strike the surface of metal A, the ejected photoelectron have maximum kinetic energy of `k_(1) eV` and the smallest de-Broglie wavelength of `lambda`. When photons of wavelength `lambda_(2) = 2640 Å` strike the surface of metal B the ejected photoelectrons have kinetic energy ranging from zero to `k_(2) = (k_(1) – 1.5) eV`. The smallest de-Broglie wavelength of electrons emitted from metal B is `2lambda`. Find (a) Work functions of metal A and B. (b) `k_(1)` Take `hc = 12410 eV Å`
Answer» Correct Answer - (a) `phi_(A) = 2.25 eV, phi_(B) = 4.2 eV` (b) `2e V`

Discussion

3.	X-ray spectrum obtained from a metallic target has been shown in the figure. The spectrum has been obtained for four different accelerating voltages in the X-ray tube: `25 kV`, `20 kV`, `15 kV` and `10 kV`. (a) Find the value of `lambda_(0)` shown in the graph. (b) What can you say about the energy of a K-shell electron in the target atom?
Answer» Correct Answer - (a) `0.08 nm` (b) Energy of an electron in `K-`shell lies between `-25 keV` and `-20 keV`.

Discussion

4.	A `mu` – meson (charge `= – e`, mass`= 208 m_(e)`) moves in a circular orbit around a heavy nucleus having charge `+ 3e`. Find the quantum state n for which the radius of the orbit is same as that of first Bohr orbit for hydrogen atom.
Answer» Correct Answer - `n = 25`

Discussion

5.	In photoelectric experiment set up, the maximum kinetic energy `(k_("max"))` of emitted photoelectrons was measured for different wavelength `(lambda)` of light used. The graph of `k_("max")` vs `1/(lambda)`   was obtained as shown in first figure. In the same setup, keeping the wavelength of incident light fixed at l, the applied potential difference was varied and the photoelectric current was recorded. The result has been shown in graph in second figure. (a) Find `lambda` is `Å` (b) Taking the photo efficiency to be `2%` (i.e. percentage of incident photons which produce photoelectrons) find the power of light incident on the emitter plate in the experiment. [Take `hc = 12400 eV Å`]
Answer» Correct Answer - (a) `5536 Å` , (b) `0.089 W`

Discussion

6.	A point source is emitting 0.2 W of ultravio- let radiation at a wavelength of `lambda = 2537 Å`. This source is placed at a distance of `1.0 m` from the cathode of a photoelectric cell. The cathode is made of potassium (Work function `= 2.22 eV`) and has a surface area of `4 cm^(2)`. (a) According to classical theory, what time of exposure to the radiation shall be required for a potassium atom to accumulate sufficient energy to eject a photoelectron. Assume that radius of each potassium atom is 2 Å and it absorbs all energy incident on it. (b) Photon flux is defined as number of light photons reaching the cathode in unit time. Calculate the photon flux. (c) Photo efficiency is defined as probability of a photon being successful in knocking out an electron from the metal surface. Calculate the saturation photocurrent in the cell assuming a photo efficiency of 0.1. (d) Find the cut – off potential difference for the cell.
Answer» Correct Answer - (a) `178 s` , (b) `8.12 xx 10^(12) s^(-1)` , (c) `65 nA` , (d) `2.68 V`

Discussion

7.	Find the change in energy of a photon of blue light `(lambda = 400 Å)` when the light enters into a medium of refractive index `mu = 4/3`.
Answer» Correct Answer - No change.

Discussion

8.	A square plate of side length L absorbs all radiation incident on it. A point source of light is placed at a point P which is directly above a corner of the plate at a height L. The incident light on the plate produces a force of magnitude `F_(0)` on the plate. Calculate the magnitude of force on the plate if the source is moved to a point Q (Q is midpoint of the line PR).
Answer» Correct Answer - `4 F_(0)`

Discussion

9.	Absorption spectrum is obtained for a sample of gas having atomic hydrogen in ground state. Which lines of the spectrum will be in the range `94 nm` to `122 nm`. Take Rydberg’s constant `R = 1.1 × 107 m^(–1)`
Answer» Correct Answer - `94.7 nm, 96.9 nm, 102.2 nm, 121 nm`

Discussion

10.	In a hypothetical hydrogen-like atom the wavelength in A° for the spectral lines for transitions from `n = P` to `n = 1` are given by `lambda = (1500 p^(2))/(p^(2) - 1)` where `p` is an integer larger than is the ionization potential of this atom ?
Answer» Correct Answer - `-8.28 eV, -2.07 eV, -0.92 eV`. Ionization Potential `= 8.28 eV`

Discussion

11.	Hydrogen like atoms (atomic number `= Z`) in a sample are in excited state with principal quantum number n. The emission spectrum of the sample has `15` different lines. The second most energetic photon emitted by the sample has energy of `27.2 eV`. Find Z.
Answer» Correct Answer - `Z = 3`

Discussion

12.	A glass tube has `Be^(+++)` ions excited to their second excited state. The radiation coming out of this tube is incident on a metal plate having work function `f = 5 eV`. Find the minimum de-Broglie wavelength of emitted photoelectrons.
Answer» Correct Answer - `0.9 Å`

Discussion

13.	Hydrogen atoms in very high quantum state have been observed in radio astronomy. The wavelength of radiation emitted when hydrogen atom makes transition from `n = 110` state to `n = 109` state is `lambda = 5.8 cm`. Imagine a He atom in which one of the electrons has been excited to `n = 110` state. What will be wavelength of emitted radiation if the electron makes transition to `n = 109`?
Answer» Correct Answer - `5.8 cm`

Discussion

14.	Radiation from hydrogen gas excited to first excited state is used for illuminating certain photoelectric plate . When the radiation from same unknown hydrogen-like gas excited to the same level is used to expose the same plate , it is found that the de Broglie wavelength of the fastest photoelectron has decreased `2.3 time`gt It is given that the energy corresponding to the longest wavelength of the Lyman series of the known gas is `3` times the ionization energy of the hydrogen gas `(13.6 eV)`. Find the work function of photoelectric plate in `eV`. `[Take (2.3)^(2) = 5.25]`
Answer» Correct Answer - `3 eV`

Discussion

15.	A perfectly absorbing solid sphere with a known fixed density, hovers stationary above the sun. This is because the gravitational attraction of the sun is balanced by the pressure due to the sun’s light. Assume the sun is far enough away so that it closely approximates a point source of light. Find the radius of the sphere and prove that it is independent of the distance of the sphere from the Sun.
Answer» Correct Answer - `R = (3p_("sun"))/(16picdGM_("sun"))`

Discussion

16.	Which of the followings can excite a hydrogen atom in ground state? (i) A photon having 11 eV energy (ii) A neutron having `11 eV` kinetic energy (iii) An electron having `11 eV` kinetic energy Give reasons for your answer.
Answer» Correct Answer - An electron having `11 eV` kinetic energy.

Discussion

17.	Assume that structure of hydrogen atom is gov- erned by classical mechanics. An electron is circulating around a proton and it is radiating energy at a rate given `(dE)/(dt) = (e^(2)a^(2))/(6pic^(3)in_(0))` where a is the acceleration of the electron. Assume that speed of the electron is `v (gt gt c)`. (a) Estimate the fraction of kinetic energy lost by the electron per revolution in terms of v. Make suitable assumptions. (b) Is the energy loss per revolution large? Is it safe to assume that orbit is circular during a small time interval?
Answer» Correct Answer - (a) `(8pi)/(3)((v)/(c))^(3)` , (b) No, Yes

Discussion

18.	Consider a gas of hydrogen atom filling a cubical box of side length 1 m. Assume that all hydrogen atoms are in their ninth excited state and they fill up the space like footballs filling up a room. Estimate the number of hydrogen atoms in the room.
Answer» Correct Answer - `8 xx 10^(23)`

Discussion

19.	A tube contains a sample of hydrogen atoms which are all in their third excited state. The atoms de-excite and a spectrum of the radiation emitted is obtained. The spectrum is shown in the given figure. (a) Which of the lines (`1, 2, 3, 4, 5` or `6`) represent a transition from quantum state `n = 3` to `n = 2`. (b) Which of the lines represent the one with second smallest wavelength?
Answer» Correct Answer - (a) `2` , (b) `5`

Discussion

20.	A proton X is projected in a region of uniform electric field E with speed u. Another proton Y is projected simultaneously with same speed u in a separate region having a uniform magnetic field ‘B’. It was found that both X and Y had same de-Broglie wavelength after time T. Specific charge on a proton is `sigma (C//kg)`.(a) Find the angle a at which the proton X was projected with respect to the direction of electric field. (b) Find the displacement of the proton X in time T.
Answer» Correct Answer - (a) `(pi)/(2) + sin^(-1) ((sigmaET)/(2u))` , (b) `sqrt(u^(2) - (sigma^(2)E^(2)T^(2))/(4)) .T`

Discussion

21.	A particle of mass m is trapped between two perfectly rigid parallel walls. The particle bounces back and forth between the walls without losing any energy. From a wave point of view, the particle trapped between the walls is like a standing wave in a stretched string between the walls. Distance between the two walls is L. (a) Calculate the energy difference between third energy state and the ground state (lowest energy state) of the particle. (b) Calculate the ground state energy if the mass of the particle is `m = 1 mg` and separation between the walls is `L = 1 cm`.
Answer» Correct Answer - (a) `(h^(2))/(mL^(2))` , (b) `5 xx 10^(-54) J`

Discussion

22.	A free hydrogen atom in its ground state is at rest. A neutron having kinetic energy `k_(0)` collides head one with the atom. Assume that mass of both neutron and the atom is same. (a) Find minimum value of `k_(0)` so that this collision can be inelastic. (b) If `k_(0) = 25 eV`, find the kinetic energy of neutron after collision if its excites the hydrogen atom to its second excited state. Take ionization energy of hydrogen atom in ground state to be `13.6 eV`.
Answer» Correct Answer - (a) `20.4 eV` , (b) `8.72 eV` or `4.19 eV`

Discussion

23.	The figure shows the reflection of a plane wave by two neighbouring atoms on the surface of a crystal. The depicted waves are actually de-Broglie wave of electrons accelerated from rest by a potential difference of V volt. Neglect relativistic effects and take mass and charge of an electron to be m and e respectively. Calculate `phi` for the case of a constructive interference.
Answer» Correct Answer - `phi = sin^(-1) ((nh)/(dsqrt(2 meV)))`

Discussion

24.	Calculate de-Broglie wavelength of hydrogen molecules `(H_(2))` present in a container at `400 K`. Assume that molecules travel at rms speed. Boltzmann constant `k = 1.38 × 10^(– 23) JK^(– 1)` Mass of `H_(2)` molecule `= 2.0 amu`
Answer» Correct Answer - `1.02Å`

Discussion

25.	A system of positron `(+1^(e^(0)))` and electron `(–1^(e^(0)))` is called Positronium atom. The radii of Positronium atom is expanded but energy levels are reduced by a factor of x compared to H – atom. (a) Find x (b) Is it true to say that the entire spectrum of Positronium will be shifted towards longer wavelength compared to H – atom.
Answer» Correct Answer - (a) `2` , (b) yes

Discussion

26.	A horizontal beam of light in incident on a plane mirror inclined at `45^(@)` to the hori- zontal. The percentage of light energy reflected from the mirror is `80%`. Find the direction in which the mirror will experience force due to the incident light.
Answer» Correct Answer - `theta = tan^(-1) (0.8)` with horizontal

Discussion

27.	A spherical concave mirror has aperture diameter d and radius of curvature R. A point source of light is placed at its centre of curvature. Source emits power W and the mirror surface is completely reflecting. Find force on the mirror due to light incident on it.
Answer» Correct Answer - `(Wd^(2))/(8R^(2)c)`

Discussion

28.	A particle of mass m is allowed to fall freely under gravity on an elastic horizontal surface. The quantum effect become important if the smallest de-Broglie wavelength of the particle is of the same order as the height from which it was dropped. Write the mechanical energy of the particle if quantum effects become important
Answer» Correct Answer - `E = ((mg^(2)h^(2))/(2))^(1//3)`

Discussion

29.	Electrons originally at rest are accelerated through a potential difference of V volts. The applied potential differ- ence is measured using a voltmeter having a least count of DV. The electrons in the beam have a de-Broglie wavelength of `lambda +- Deltalambda [Deltalambda ltlt]`. Find `\|(Deltalambda)/(lambda)\|`.
Answer» Correct Answer - `(Deltalambda)/(lambda) = (DeltaV)/(2V)`

Discussion

Explore topic-wise InterviewSolutions in .

A `mu` – meson (charge `= – e`, mass`= 208 m_(e)`) moves in a circular orbit around a heavy nucleus having charge `+ 3e`. Find the quantum state n for which the radius of the orbit is same as that of first Bohr orbit for hydrogen atom.

Find the change in energy of a photon of blue light `(lambda = 400 Å)` when the light enters into a medium of refractive index `mu = 4/3`.

Absorption spectrum is obtained for a sample of gas having atomic hydrogen in ground state. Which lines of the spectrum will be in the range `94 nm` to `122 nm`. Take Rydberg’s constant `R = 1.1 × 107 m^(–1)`

In a hypothetical hydrogen-like atom the wavelength in A° for the spectral lines for transitions from `n = P` to `n = 1` are given by `lambda = (1500 p^(2))/(p^(2) - 1)` where `p` is an integer larger than is the ionization potential of this atom ?

Hydrogen like atoms (atomic number `= Z`) in a sample are in excited state with principal quantum number n. The emission spectrum of the sample has `15` different lines. The second most energetic photon emitted by the sample has energy of `27.2 eV`. Find Z.

A glass tube has `Be^(+++)` ions excited to their second excited state. The radiation coming out of this tube is incident on a metal plate having work function `f = 5 eV`. Find the minimum de-Broglie wavelength of emitted photoelectrons.

Which of the followings can excite a hydrogen atom in ground state? (i) A photon having 11 eV energy (ii) A neutron having `11 eV` kinetic energy (iii) An electron having `11 eV` kinetic energy Give reasons for your answer.

Consider a gas of hydrogen atom filling a cubical box of side length 1 m. Assume that all hydrogen atoms are in their ninth excited state and they fill up the space like footballs filling up a room. Estimate the number of hydrogen atoms in the room.

Calculate de-Broglie wavelength of hydrogen molecules `(H_(2))` present in a container at `400 K`. Assume that molecules travel at rms speed. Boltzmann constant `k = 1.38 × 10^(– 23) JK^(– 1)` Mass of `H_(2)` molecule `= 2.0 amu`

A horizontal beam of light in incident on a plane mirror inclined at `45^(@)` to the hori- zontal. The percentage of light energy reflected from the mirror is `80%`. Find the direction in which the mirror will experience force due to the incident light.

A spherical concave mirror has aperture diameter d and radius of curvature R. A point source of light is placed at its centre of curvature. Source emits power W and the mirror surface is completely reflecting. Find force on the mirror due to light incident on it.