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Chapter 2: Problem 91

If \(\mathrm{S}\), be the specific charge \((\mathrm{e} / \mathrm{m})\) of cathode rays and \(\mathrm{S}_{2}\) be that of positive rays then which is true? (a) \(\mathrm{S}_{1}=\mathrm{S}_{2}\) (b) \(\mathrm{S}_{1}<\mathrm{S}_{2}\) (c) \(\mathrm{S}_{1}>\mathrm{S}_{2}^{-}\) (d) None of these

Short Answer

Expert verified
(c) \( \mathrm{S}_1 > \mathrm{S}_2 \)

Step by step solution

01

Understand What Specific Charge Is

Specific charge is the charge-to-mass ratio of a particle. It is calculated as \( \frac{e}{m} \), where \( e \) is the charge of the particle and \( m \) is its mass.
02

Definition of Cathode Rays and Positive Rays

Cathode rays are streams of electrons emitted from the cathode in a vacuum tube, so their specific charge \( S_1 \) is determined by the electron's charge and mass. Positive rays, on the other hand, consist of positive ions, whose specific charge \( S_2 \) depends on the ion's charge and mass.
03

Comparing Masses of Electrons and Ions

Typically, the mass of an electron is much smaller than the mass of the ions that make up positive rays since ions are composed of atoms or molecules. This implies that electrons have a higher specific charge due to their smaller mass.
04

Comparing Specific Charges

Given that \( S_1 \) (specific charge of cathode rays) involves the small mass of an electron while \( S_2 \) (specific charge of positive rays) involves the larger mass of ions, it follows that \( S_1 > S_2 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Cathode Rays
Cathode rays are an important concept in the study of atomic physics. These rays are essentially streams of electrons that are emitted from the cathode of a vacuum tube when a high voltage is applied across it.

In a cathode ray tube, when the electrical potential difference is applied, it causes electrons to accelerate and form a stream known as cathode rays.

This revolutionary discovery was pivotal in understanding the nature of electrons and helped shape the field of electronics. Since electrons are the primary constituents of cathode rays, their specific charge is primarily determined by the properties of electrons themselves. Cathode rays possess a high specific charge because the mass of electrons (which they are composed of) is extremely small.
Positive Rays
Also referred to as canal rays, positive rays are composed of positive ions. They are observed in specialized glass tubes known as discharge tubes.

While cathode rays consist of negatively charged electrons, positive rays consist of positively charged ions, such as protons and other heavier ions. The charge-to-mass ratio of positive rays tends to be much lower because ions are much heavier compared to electrons.

Positive rays migrate towards the negatively charged electrode (cathode) in discharge tubes because of their positive charge, demonstrating the opposite behavior to cathode rays in electric fields.
Charge-to-Mass Ratio
The charge-to-mass ratio is a fundamental concept in physics to describe how much charge is contained per unit mass of a particle. This ratio is denoted as \(\frac{e}{m}\), where \(e\) is the charge and \(m\) is the mass.

This ratio is especially significant when analyzing particles like electrons and ions to predict their behaviors under electric and magnetic fields.

Electrons, because of their smaller mass, have a large charge-to-mass ratio, while ions, being heavier, exhibit a smaller ratio. This key difference allows scientists to differentiate between various types of particles based on their specific charge values.
Electron Mass
The mass of an electron is one of the defining features of its behavior in an electromagnetic field. Electrons possess an extremely small mass of approximately \(9.109 \times 10^{-31}\) kilograms.

This small mass plays a crucial role in giving electrons (and thereby cathode rays) a high specific charge.

Understanding the mass of an electron is essential for calculating various phenomena in physics, such as in determining the wavelength of particles in quantum mechanics or the force experienced by electrons in a magnetic field.
Ion Mass
Ions, in contrast to electrons, have a much larger mass due to being composed of one or more atoms. The mass of ions can vary greatly depending on the element or molecule from which they are derived.

For instance, a proton (the simplest form of an ion) has a mass of approximately \(1.673 \times 10^{-27}\) kilograms. This mass is significantly larger than that of an electron.
  • Due to their larger mass, ions have a lower charge-to-mass ratio than electrons.
  • This fact is crucial when comparing specific charges as ions will tend to deflect less in magnetic fields compared to electrons.
Understanding ion mass is key in fields such as mass spectrometry, where differentiating ions based on their charge-to-mass ratio is fundamental.

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Most popular questions from this chapter

The de Broglie wavelength of the electron in the ground state of hydrogen atom is \([\mathrm{K} . \mathrm{E} .=13.6 \mathrm{eV}]\); \(\mathrm{leV}=1.602 \times 10^{-19} \mathrm{~J}\) (a) \(33.28 \mathrm{~nm}\) (b) \(3.328 \mathrm{~nm}\) (c) \(0.3328 \mathrm{~nm}\) (d) \(0.0332 \mathrm{~nm}\)

Quantum numbers of an atom can be defined on the basis of: (a) Aufbau's principle (b) Heisenberg's uncertainity principle (c) Hund's rule (d) Pauli's exclusion principle

The quantum number \(+\frac{1}{2}\) and \(-\frac{1}{2}\) for the electron spin represent: (a) Rotation of the electron in clockwise and anticlockwise direction respectively. (b) Rotation of the electron in anti clockwise and clockwise direction respectively. (c) Magnetic moment of the electron pointing up and down respectively. (d) Two quantum mechanical spin states which have no classical analogues.

The correct order of number of unpaired electrons in the ion \(\mathrm{Cu}^{2+} \mathrm{Ni}^{2+}, \mathrm{Fe}^{3+}\) and \(\mathrm{Cr}^{3+}\) is: (a) \(\mathrm{Cu}^{2+}>\mathrm{Ni}^{2+}>\mathrm{Cr}^{3+}>\mathrm{Fe}^{3+}\) (b) \(\mathrm{Ni}^{2+}>\mathrm{Cu}^{2+}>\mathrm{Fe}^{3+}>\mathrm{Cr}^{3+}\) (c) \(\mathrm{Fe}^{3+}>\mathrm{Cr}^{3+}>\mathrm{Ni}^{2+}>\mathrm{Cu}^{2+}\) (d) \(\mathrm{Fe}^{3+}>\mathrm{Cr}^{3+}>\mathrm{Cu}^{2+}>\mathrm{Ni}^{2+}\)

Calculate the wavelength and energy of the radiation emitted for the electronic transition from infinity \((\infty)\) to stationary state first of the hydrogen atom. \(\left(\mathrm{R}_{\mathrm{H}}=1.09678 \times 10^{7} \mathrm{~m}^{-1}, \mathrm{~h}=6.6256 \times 10^{-34} \mathrm{Js}\right)\) (a) \(2.18 \times 10^{-21} \mathrm{~kJ}\) (b) \(3.18 \times 10^{-22} \mathrm{~kJ}\) (c) \(1.18 \times 10^{-23} \mathrm{~kJ}\) (d) \(2.18 \times 10^{-31} \mathrm{~kJ}\)
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