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 Multiple Choice QuestionsMultiple Choice Questions

1.

The hydrogen atom is excited from ground state to another state with the principal quantum number equal to 4. Then the number of spectral lines in the emission spectra will be

  • 2

  • 3

  • 3

  • 3


D.

3

Number of spectral lines from a state n to ground state is

fraction numerator straight n left parenthesis straight n minus 1 right parenthesis over denominator 2 end fraction space equals space fraction numerator 4 left parenthesis straight n minus 1 right parenthesis over denominator 2 end fraction space equals space 6

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2.

The radiation corresponding to 3 → 2 transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field of 3 x 10-4 T. If the radius of the largest the circular path followed by these electrons is 10.0 mm, the work function of the metal is close to:

  • 1.8 eV

  • 1.1 eV

  • 0.8 eV

  • 0.8 eV


B.

1.1 eV

mv =qBR

KE subscript max space equals space fraction numerator open parentheses mv close parentheses squared over denominator 2 straight m end fraction space equals space 0. space 8 space eV
hv space equals space 13.6 space open square brackets 1 fourth minus 1 over 6 close square brackets
therefore space straight w space equals space hv minus KE subscript max
space equals space 13.6 5 over 36 minus 0.8 space equals space 1.1 space eV

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3.

The energy spectrum of β-particles [number N(E) as a function of β-energy E] emitted from a radioactive source is


C.

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4.

The potential energy function for the force between two atoms in a diatomic molecule is approximately given by straight U left parenthesis straight x right parenthesis space equals space straight a over straight x to the power of 12 minus straight b over straight x to the power of 16 where a and b are constants and x is the distance between the atoms. If the dissociation energy of the molecule is D = [U(x = ∞) – Uat equilibrium], D is

  • b2/2a

  • b2/12a

  • b2/4a

  • b2/4a


C.

b2/4a

The potential energy for diatomic molecule is 
straight U left parenthesis straight x right parenthesis space equals space straight a over straight x to the power of 12 minus straight b over straight x to the power of 6
straight U space left parenthesis straight x space equals space infinity right parenthesis space equals space 0
As comma space straight F space equals space minus space dU over dx space equals space minus space open square brackets fraction numerator 12 straight a over denominator straight x to the power of 13 end fraction plus fraction numerator 6 straight b over denominator straight x to the power of 7 end fraction close square brackets
At space equilibrium comma space straight F space equals space 0
therefore space straight x to the power of 6 space equals space fraction numerator 2 straight a over denominator straight b end fraction
therefore space straight U subscript at space equilibrium end subscript space equals space straight a over open parentheses begin display style fraction numerator 2 straight a over denominator straight b end fraction end style close parentheses squared space minus space fraction numerator straight b over denominator open parentheses begin display style fraction numerator 2 straight a over denominator straight b end fraction end style close parentheses end fraction space equals space fraction numerator negative straight b squared over denominator 4 straight a end fraction
therefore space straight D space equals space left square bracket space straight U space left parenthesis straight x equals space infinity right parenthesis minus straight U subscript at space equilibrium space right square bracket space end subscript space equals space fraction numerator straight b squared over denominator 4 straight a end fraction

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5.

The diagram shows the energy levels for an electron in a certain atom. Which transition shown represents the emission of a photon with the most energy?

  • lll

  • IV

  • I

  • I


A.

lll

increment straight E space proportional to open parentheses fraction numerator 1 over denominator straight n subscript 1 superscript 2 end fraction minus fraction numerator 1 over denominator straight n subscript 2 superscript 2 end fraction close parentheses
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6.

Energy required for the electron excitation in Li++ from the first to the third Bohr orbit is

  • 36.3 eV

  • 108.8 eV

  • 122.4 eV

  • 122.4 eV


B.

108.8 eV

increment straight E space equals space 13.6 space straight Z squared space open parentheses fraction numerator 1 over denominator straight n subscript 1 superscript 2 end fraction minus fraction numerator 1 over denominator straight n subscript 2 superscript 2 end fraction close parentheses
space equals space 13.6 space left parenthesis 3 right parenthesis squared space open parentheses 1 over 1 squared minus 1 over 3 squared close parentheses space equals space 108.8 space eV
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7.

Which of the following transitions in hydrogen atoms emit photons of highest frequency?

  • n = 2 to n = 6

  • n = 6 to n = 2

  • n = 2 to n =1

  • n = 2 to n =1


C.

n = 2 to n =1

203 Views

8.

In a hydrogen like atom, electron makes the transition from an energy level with quantum number n to another with a quantum number (n – 1). If n >> 1, the frequency of radiation emitted is proportional to 

  • 1/n

  • 1/n2

  • 1/n3/2

  • 1/n3/2


D.

1/n3/2

An energy gap, ΔE = hv
Here, h is Planck's constant
therefore,
Frequency
straight v space equals space fraction numerator increment straight E over denominator straight h end fraction space equals space straight k space open square brackets fraction numerator 1 over denominator left parenthesis straight n minus 1 right parenthesis squared end fraction minus 1 over straight n squared close square brackets
rightwards double arrow space straight v space equals fraction numerator straight k 2 straight n over denominator straight n squared left parenthesis straight n minus 1 right parenthesis squared end fraction space
straight v space proportional to 1 over straight n cubed

398 Views

9.

If a source of power 4kW produces 1020 photons/second, the radiation belongs to a part of the spectrum called

  • X -rays

  • ultraviolet rays

  • microwaves

  • microwaves


A.

X -rays

As power of source = 4 x 103 = 1020 x hv
(∴ P/E = Number of photons)

straight v equals space fraction numerator 4 space straight x space 10 cubed over denominator 10 to the power of 20 space straight x space 6.023 space straight x space 10 to the power of negative 34 end exponent end fraction
space straight v space equals space 6.64 space straight x space 10 to the power of 16 space Hz

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10.

Suppose an electron is attracted towards the origin by a force k/r where ‘k’ is a constant and ‘r’ is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the nth orbital of the electron is found to be ‘rn’ and the kinetic energy of the electron to be Tn. Then which of the following is true?

  • Tn ∝ 1/n2, rn ∝ n2 

  • Tn independent of n, rn ∝ n

  • Tn ∝ 1/n, rn ∝ n 

  • Tn ∝ 1/n, rn ∝ n 


B.

Tn independent of n, rn ∝ n

straight k over straight r space equals space mv squared over straight r
mv squared space equals space straight k space space left parenthesis independent space or space straight r right parenthesis
straight n open parentheses fraction numerator straight h over denominator 2 straight pi end fraction close parentheses space equals space mvr
rightwards double arrow space straight r proportional to space straight n
and space straight T space equals space 1 half mv squared space space is space independent space of space straight n.
370 Views