Electrons in a cathode ray tube have been emitted with a velocity of \(1000\, m s ^{-1}\). The number of following statements which is/are true about the emitted radiation is _______ Given : \(h =6 \times 10^{-34} J s , m _e=9 \times 10^{-31} kg\)
(A) The deBroglie wavelength of the electron emitted is \(66667 nm\)
(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
(A) The deBroglie wavelength of the electron emitted is \(66667 nm\)
(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
Show Hint
The de Broglie wavelength of a particle is inversely proportional to its momen tum (p = mv), and it helps describe wave-particle duality
Correct Answer: 2
Approach Solution - 1
Analysis of Statements:
- Statement (A): The de Broglie wavelength (λ) is calculated using the formula:
λ = h / mv
Substituting the given values:
\(λ = \frac{(6 × 10−34) }{ (9 × 10−31 × 1000)}\)
λ = 6.67 × 10−7 m = 666.67 nm.
This statement is true. - Statement (B): The emission of electrons in a cathode ray tube depends on the material of the cathode, as the work function and the energy required to emit electrons vary with the material.
This statement is true. - Statement (C): Cathode rays are streams of electrons that start from the cathode (negative electrode) and travel towards the anode (positive electrode) in a cathode ray tube.
This statement is true. - Statement (D): The electrons themselves are not affected by the nature of the gas present in the cathode ray tube. The nature of the gas may affect the fluorescence or color of the emitted light, but not the nature of the electrons.
This statement is false.
Conclusion: The number of true statements is 2 (A and B).
Approach Solution -2
(A) ;
(B) The characteristic of electrons emitted is independent of 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 is independent on the nature of the gas present in cathode ray tube.
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Concepts Used:
Atoms
- The smallest unit of matter indivisible by chemical means is known as an atom.
- The fundamental building block of a chemical element.
- The smallest possible unit of an element that still has all the chemical properties of that element.
- An atom is consisting of a nucleus surrounded by one or more shells of electrons.
- Word origin: from the Greek word atomos, which means uncuttable, something that cannot be divided further.
All matter we encounter in everyday life consists of smallest units called atoms – the air we breath consists of a wildly careening crowd of little groups of atoms, my computer’s keyboard of a tangle of atom chains, the metal surface it rests on is a crystal lattice of atoms. All the variety of matter consists of less than hundred species of atoms (in other words: less than a hundred different chemical elements).
Every atom consists of an nucleus surrounded by a cloud of electrons. Nearly all of the atom’s mass is concentrated in its nucleus, while the structure of the electron cloud determines how the atom can bind to other atoms (in other words: its chemical properties). Every chemical element can be defined via a characteristic number of protons in its nucleus. Atoms that have lost some of their usual number of electrons are called ions. Atoms are extremely small (typical diameters are in the region of tenths of a billionth of a metre = 10-10 metres), and to describe their properties and behaviour, one has to resort to quantum theory.