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Structure of Atom question

2023 · 1 Feb · Shift 1 · Q13
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Structure of Atom question

2023 · 1 Feb · Shift 1 · Q13

JEE MainChemistryStructure of AtomNumerical+4 / −1
Electrons in a cathode ray tube have been emitted with a velocity of 1000 m s −1^{-1}−1. The number of following statements which is/are true‾\underline {\mathrm{true}}true​ about the emitted radiation is ‾\underline{\hspace{2cm}}​. Given : h=6×10−34 J s,me=9×10−31 kg\mathrm{h=6\times10^{-34}~J~s,m_e=9\times10^{-31}~kg}h=6×10−34 J s,me​=9×10−31 kg. (A) The de-Broglie wavelength of the electron emitted is 666.67 nm. (B) The characteristic of electrons emitted depend upon the material of the electrodes of the cathode ray tube. (C) The cathode rays start from cathode and move towards anode. (D) The nature of the emitted electrons depends on the nature of the gas present in cathode ray tube.
Numerical answer
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Correct answer: 2

  1. We need to count how many statements are true.

  2. Check statement (A): de-Broglie wavelength

    The de-Broglie wavelength is λ=hmv\lambda = \frac{h}{mv}λ=mvh​

    Given: h=6×10−34 J s,m=9×10−31 kg,v=1000 m s−1=103 m s−1h=6\times 10^{-34}\ \text{J s},\quad m=9\times 10^{-31}\ \text{kg},\quad v=1000\ \text{m s}^{-1} = 10^3\ \text{m s}^{-1}h=6×10−34 J s,m=9×10−31 kg,v=1000 m s−1=103 m s−1

    So, λ=6×10−34(9×10−31)(103)\lambda = \frac{6\times 10^{-34}}{(9\times 10^{-31})(10^3)}λ=(9×10−31)(103)6×10−34​ λ=6×10−349×10−28\lambda = \frac{6\times 10^{-34}}{9\times 10^{-28}}λ=9×10−286×10−34​ λ=23×10−6 m\lambda = \frac{2}{3}\times 10^{-6}\ \text{m}λ=32​×10−6 m λ=0.6667×10−6 m=6.667×10−7 m\lambda = 0.6667\times 10^{-6}\ \text{m} = 6.667\times 10^{-7}\ \text{m}λ=0.6667×10−6 m=6.667×10−7 m

    Since 1 nm=10−9 m1\ \text{nm} = 10^{-9}\ \text{m}1 nm=10−9 m λ=666.7 nm\lambda = 666.7\ \text{nm}λ=666.7 nm

    Hence, (A) is true.

  3. Check statement (B): dependence on electrode material

    Cathode rays are streams of electrons. Their fundamental properties do not depend on the material of the electrodes.

    Hence, (B) is false.

  4. Check statement (C): direction of cathode rays

    Cathode rays are emitted from the cathode and move toward the anode.

    Hence, (C) is true.

  5. Check statement (D): dependence on gas present in tube

    The nature of cathode rays (electrons) does not depend on the nature of the gas in the discharge tube.

    Hence, (D) is false.

  6. Total number of true statements:

    True statements are (A) and (C).

    Therefore, the number of true statements is 222

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