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Test: Dual Behaviour of Matter, Heisenberg Uncertainty Principle - JEE MCQ


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15 Questions MCQ Test - Test: Dual Behaviour of Matter, Heisenberg Uncertainty Principle

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Test: Dual Behaviour of Matter, Heisenberg Uncertainty Principle - Question 1

If a suitable photon is employed to locate an electron (mass = 9.11 × 10−31 kg) in an atom within a distance of 10.98 nm, the uncertainty involved in the measurement of its velocity in ms−1 is

Detailed Solution for Test: Dual Behaviour of Matter, Heisenberg Uncertainty Principle - Question 1

Given,
Mass of electron = 9.11  ×10−31 kg
Position of electron = 10.98 nm
= 10.98 × 10−9 m
Here, Planck constant = 6.63 × 10−34Js
Δv = ?
According to Heisenberg uncertainty

Test: Dual Behaviour of Matter, Heisenberg Uncertainty Principle - Question 2

The position of both, an electron and a helium atom is known within . Further the momentum of the electron is known within . The minimum uncertainty in the measurement of the momentum of the helium atom is

Detailed Solution for Test: Dual Behaviour of Matter, Heisenberg Uncertainty Principle - Question 2

According to Heisenberg uncertainty principle,
(which is constant).
As Δx for electron and helium atom is same, thus momentum of electron and helium will also be same, therefore the momentum of helium atom is equal to 5 × 10−26 kg ms−1.

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Test: Dual Behaviour of Matter, Heisenberg Uncertainty Principle - Question 3

At temperature T, the average kinetic energy of any particle is .  The de Broglie wavelength follows the order:

Detailed Solution for Test: Dual Behaviour of Matter, Heisenberg Uncertainty Principle - Question 3

Kinetic energy of any particle
Also K.E.




De-broglie wavelength


Mass of electron < mass of neutron λ (electron) >λ (neutron)

Test: Dual Behaviour of Matter, Heisenberg Uncertainty Principle - Question 4

The de-Broglie wavelength of a tennis ball of mass 60 g moving with a velocity of 10 ms−1 is approximately ____ (Planck's constant h = 6.63 × 10−34 J.s)

Detailed Solution for Test: Dual Behaviour of Matter, Heisenberg Uncertainty Principle - Question 4

de-Broglie's wave equation is

Test: Dual Behaviour of Matter, Heisenberg Uncertainty Principle - Question 5
According to Bohr's theory which one of the following values of angular momentum of hydrogen atom is not permitted?
Detailed Solution for Test: Dual Behaviour of Matter, Heisenberg Uncertainty Principle - Question 5
According to Bohr's model, electrons revolve only in those orbits for which angular momentum is an integral multiple of i.e.,
Test: Dual Behaviour of Matter, Heisenberg Uncertainty Principle - Question 6

If the de-Broglie wavelength of a particle of mass m is 100 times its velocity, then its value in terms of its mass (m) and Planck's constant (h) is

Detailed Solution for Test: Dual Behaviour of Matter, Heisenberg Uncertainty Principle - Question 6

Let wavelength of particle be x

Test: Dual Behaviour of Matter, Heisenberg Uncertainty Principle - Question 7

Calculate the velocity of ejected electron from the metal surface when light of frequency fall on the metal surface and the threshold frequency is for metal ?

Detailed Solution for Test: Dual Behaviour of Matter, Heisenberg Uncertainty Principle - Question 7

Test: Dual Behaviour of Matter, Heisenberg Uncertainty Principle - Question 8

Two fast moving particles and are associated with de Broglie wavelengths and respectively. If mass of is nine times the mass of , the ratio of kinetic energies of and would be

Detailed Solution for Test: Dual Behaviour of Matter, Heisenberg Uncertainty Principle - Question 8

de Broglie wavelength



Test: Dual Behaviour of Matter, Heisenberg Uncertainty Principle - Question 9

The energy required to remove an electron from the surface of Sodium metal is What is the longest wavelength of radiation with which it can show photoelectric effect?

Detailed Solution for Test: Dual Behaviour of Matter, Heisenberg Uncertainty Principle - Question 9

Energy required to show photo emission

Thus

Thus, longest wavelength to show photoelectric effect

Test: Dual Behaviour of Matter, Heisenberg Uncertainty Principle - Question 10

The velocity of particle is and that of particle is If the mass of particle is five times that of particle , then the ratio of deBroglie wavelengths associated with the particles and is

Detailed Solution for Test: Dual Behaviour of Matter, Heisenberg Uncertainty Principle - Question 10

Given, and also,

de-Broglie wavelength,


Test: Dual Behaviour of Matter, Heisenberg Uncertainty Principle - Question 11

A light of frequency when falls on a metal plate emits electrons that have double the kinetic energy compared to the kinetic energy of emitted electrons when frequency of falls on the same plate. The threshold frequency of the metal in is

Detailed Solution for Test: Dual Behaviour of Matter, Heisenberg Uncertainty Principle - Question 11

When 1.6 × 1016 Hz frequency falls on metal plate than double kinetic energy obtained.
h(1.6 × 1016 − v0) = 2 K.E⟶ Eq. (i) 
When 1.0 × 1016 Hz frequency falls on same plate than K.E.
h(1.0 × 1016 − v0)= K.E ⟶ (Eq. (ii))
From Eqs. (i) and (ii)

Test: Dual Behaviour of Matter, Heisenberg Uncertainty Principle - Question 12

The work function (ϕ) of some metals is listed below. The number of metals which will show photoelectric effect when light of 300 nm wavelength falls on the metals is:

Detailed Solution for Test: Dual Behaviour of Matter, Heisenberg Uncertainty Principle - Question 12

Energy of photon

For photoelectric effect to occur, energy of incident photons, must be greater than work functions of metal. Hence, only Li, Na, K and Mg have work functions less than 4.14 V.

Test: Dual Behaviour of Matter, Heisenberg Uncertainty Principle - Question 13
Which of the following graphs correctly represents the variation of particle momentum with associated de Broglie wavelength?
Detailed Solution for Test: Dual Behaviour of Matter, Heisenberg Uncertainty Principle - Question 13
there is inverse relation between de Broglie wavelength and momentum, hence the graph will be rectangular hyperbola.
Test: Dual Behaviour of Matter, Heisenberg Uncertainty Principle - Question 14

If uncertainty in position and velocity are equal then uncertainty in momentum will be

Detailed Solution for Test: Dual Behaviour of Matter, Heisenberg Uncertainty Principle - Question 14

Test: Dual Behaviour of Matter, Heisenberg Uncertainty Principle - Question 15
Which of the following plot is correct about the kinetic energy of photoelectrons?
Detailed Solution for Test: Dual Behaviour of Matter, Heisenberg Uncertainty Principle - Question 15
Here plot in option A is correct as Kinetic energy of photoelectrons is independent of the intensity of radiation.
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